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': '12.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [3, 6, 12, 12], 'aut_gens': [[1, 6, 36, 648, 5832, 17496, 52488, 157464], [421369, 356262, 15804, 2592, 19872, 49032, 52488, 202392], [138187, 431526, 54846, 23400, 313416, 447336, 15552, 85536], [199453, 359310, 146286, 21960, 311256, 445608, 21384, 81648], [85253, 238614, 57870, 8280, 443664, 309312, 7776, 97200]], 'aut_group': None, 'aut_hash': 7790605820590529493, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 8503056, 'aut_permdeg': 864, 'aut_perms': 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'aut_phi_ratio': 54.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 54, 1, 1], [2, 486, 1, 1], [2, 729, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 2], [3, 4, 2, 5], [3, 8, 1, 1], [3, 8, 2, 1], [3, 36, 1, 1], [3, 36, 2, 1], [3, 36, 18, 1], [3, 72, 1, 1], [3, 72, 2, 1], [3, 72, 18, 1], [3, 324, 1, 1], [3, 324, 6, 1], [3, 648, 3, 1], [3, 648, 6, 3], [4, 13122, 1, 1], [6, 54, 2, 4], [6, 108, 1, 1], [6, 108, 2, 4], [6, 486, 2, 1], [6, 729, 2, 1], [6, 972, 1, 2], [6, 972, 2, 2], [6, 972, 18, 1], [6, 1458, 1, 1], [6, 1458, 2, 1], [6, 8748, 1, 1], [6, 8748, 6, 1], [9, 18, 18, 1], [9, 36, 3, 1], [9, 36, 6, 1], [9, 36, 18, 1], [9, 72, 3, 1], [9, 72, 6, 1], [9, 81, 6, 1], [9, 162, 3, 1], [9, 162, 6, 2], [9, 324, 3, 1], [9, 324, 6, 1], [9, 324, 18, 3], [9, 648, 3, 2], [9, 648, 18, 1], [12, 13122, 2, 1], [18, 54, 18, 1], [18, 108, 18, 1], [18, 486, 6, 6], [18, 486, 18, 1], [18, 729, 6, 1], [18, 972, 3, 1], [18, 972, 6, 2], [18, 972, 18, 3], [18, 1458, 3, 1], [18, 1458, 6, 2], [18, 1458, 18, 1], [18, 4374, 6, 1], [18, 8748, 3, 1], [36, 13122, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^5.C_3^4.C_2.C_6^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 3, 'autcent_group': '3.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 3, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': None, 'autcentquo_hash': 442385174167179022, 'autcentquo_nilpotent': False, 'autcentquo_order': 2834352, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^5.C_3^4.C_6^2.C_2^2', 'cc_stats': [[1, 1, 1], [2, 54, 1], [2, 486, 1], [2, 729, 1], [3, 1, 2], [3, 2, 3], [3, 4, 12], [3, 8, 3], [3, 36, 21], [3, 72, 21], [3, 324, 7], [3, 648, 21], [4, 13122, 1], [6, 54, 8], [6, 108, 9], [6, 486, 2], [6, 729, 2], [6, 972, 24], [6, 1458, 3], [6, 8748, 7], [9, 18, 18], [9, 36, 27], [9, 72, 9], [9, 81, 6], [9, 162, 15], [9, 324, 63], [9, 648, 24], [12, 13122, 2], [18, 54, 18], [18, 108, 18], [18, 486, 54], [18, 729, 6], [18, 972, 69], [18, 1458, 33], [18, 4374, 6], [18, 8748, 3], [36, 13122, 6]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 465, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 54, 1, 1], [2, 486, 1, 1], [2, 729, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 2], [3, 4, 2, 5], [3, 8, 1, 1], [3, 8, 2, 1], [3, 36, 1, 1], [3, 36, 2, 10], [3, 72, 1, 1], [3, 72, 2, 10], [3, 324, 1, 1], [3, 324, 2, 3], [3, 648, 1, 3], [3, 648, 2, 9], [4, 13122, 1, 1], [6, 54, 2, 4], [6, 108, 1, 1], [6, 108, 2, 4], [6, 486, 2, 1], [6, 729, 2, 1], [6, 972, 1, 2], [6, 972, 2, 11], [6, 1458, 1, 1], [6, 1458, 2, 1], [6, 8748, 1, 1], [6, 8748, 2, 3], [9, 18, 6, 3], [9, 36, 3, 1], [9, 36, 6, 4], [9, 72, 3, 1], [9, 72, 6, 1], [9, 81, 6, 1], [9, 162, 3, 1], [9, 162, 6, 2], [9, 324, 3, 1], [9, 324, 6, 10], [9, 648, 3, 2], [9, 648, 6, 3], [12, 13122, 2, 1], [18, 54, 6, 3], [18, 108, 6, 3], [18, 486, 6, 9], [18, 729, 6, 1], [18, 972, 3, 1], [18, 972, 6, 11], [18, 1458, 3, 1], [18, 1458, 6, 5], [18, 4374, 6, 1], [18, 8748, 3, 1], [36, 13122, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [10, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 36], [24, 0, 18], [36, 0, 36], [72, 0, 24]], 'familial': False, 'frattini_label': '729.504', 'frattini_quotient': '648.719', 'hash': 4458908981959553522, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [12, 18, 18, 9, 3, 3, 3, 3], 'inner_gens': [[1, 3342, 36846, 15840, 258984, 392904, 23328, 134136], [113773, 6, 466092, 448416, 39096, 13824, 445176, 181224], [263035, 388014, 36, 5184, 17496, 50544, 104976, 202176], [22393, 53790, 1332, 648, 5832, 17496, 256608, 157464], [453169, 25710, 40860, 648, 5832, 17496, 52488, 157464], [278425, 27654, 42804, 648, 5832, 17496, 52488, 157464], [99145, 312990, 105012, 338904, 5832, 17496, 52488, 157464], [250777, 46878, 31140, 648, 5832, 17496, 52488, 157464]], 'inner_hash': 7921234277888382341, 'inner_nilpotent': False, 'inner_order': 157464, 'inner_split': None, 'inner_tex': 'C_3^5.C_3^2.C_6^2.C_2', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': None, 'irrep_stats': [[1, 12], [2, 15], [4, 24], [6, 72], [8, 3], [9, 24], [12, 96], [18, 66], [24, 30], [36, 140], [72, 45]], 'label': '472392.rw', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6.C3wrD4', 'ngens': 13, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 91, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 527, 'number_divisions': 153, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 6482, 'number_subgroup_classes': 22867, 'number_subgroups': 6605386, 'old_label': None, 'order': 472392, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1269], [3, 18224], [4, 13122], [6, 92772], [9, 40824], [12, 26244], [18, 201204], [36, 78732]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [3, 3, 6], 'outer_gen_pows': [0, 153777, 247482], 'outer_gens': [[183685, 163878, 46692, 4536, 50760, 9936, 52488, 189000], [13915, 323454, 189126, 8280, 105408, 309312, 23760, 217728], [85253, 238614, 57870, 8280, 443664, 309312, 7776, 97200]], 'outer_group': '54.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 54, 'outer_permdeg': 54, 'outer_perms': [12833960214435027446871896023184740056976945617873744619086807371262738, 30811795187680700074273234709006228436182273458636991667177998088764880, 17513899101424228912470384346025745215339414663091156624125056914595056], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2\\times C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 7], [4, 10], [8, 11], [12, 2], [16, 1], [24, 21], [36, 16], [48, 10], [54, 6], [72, 18], [108, 12], [144, 10], [216, 22], [432, 3]], 'representations': {'PC': {'code': '1913159035548683783949514701681308313086294190635133503032809555787695753235012466768307815594653223503548772606598266548738760867799559972299841381544068171770426501717558320475422670298292555491523578162104944909598842768050467632437296286363906133287524563143175833226241838524858286095550922838578197100936484701511106047610068124822271', 'gens': [1, 3, 5, 8, 10, 11, 12, 13], 'pres': [13, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 26, 5532008, 130340, 8133504, 106, 5785731, 2791480, 1524786, 2394994, 4933907, 5049360, 392188, 186, 8592485, 620586, 307975, 103004, 304, 353814, 19675, 6584, 1647367, 20386100, 7772577, 3880702, 15035, 410, 25280, 227469, 75850, 12696, 33667929, 2541262, 847115, 65568, 63241, 91334, 56185282, 988439, 329508, 211117, 200834, 19380, 3639179, 8491416, 11574613, 707666, 454959, 61878, 22668996, 15313453, 5104514, 2223753, 949168, 442688]}, 'Perm': {'d': 36, 'gens': [42542289011529293660795865902283494012156, 371689682145656058330549881741098566025085]}}, 'schur_multiplier': [2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 486, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.C_3\\wr D_4', 'transitive_degree': 36, 'wreath_data': ['(C_3.C_3{\rm wrC}_3):C_2', 'C_2', '2T1'], 'wreath_product': True}

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
Showing the first 100 of 527 matching records in this table.

id: 162870691
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 465, 'group_order': 472392, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 162870802
{'aut_label': '2A', 'centralizer': '54.F', 'counter': 2, 'group_counter': 465, 'group_order': 472392, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 2268, 'size': 54}
id: 162870913
{'aut_label': '2B', 'centralizer': '486.BQ', 'counter': 3, 'group_counter': 465, 'group_order': 472392, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 47445, 'size': 486}
id: 162871024
{'aut_label': '2C', 'centralizer': None, 'counter': 4, 'group_counter': 465, 'group_order': 472392, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 113850, 'size': 729}
id: 162871135
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 465, 'group_order': 472392, 'label': '3A1', 'order': 3, 'powers': [6, 1], 'representative': 165240, 'size': 1}
id: 162871174
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 465, 'group_order': 472392, 'label': '3A-1', 'order': 3, 'powers': [5, 1], 'representative': 330480, 'size': 1}
id: 162871185
{'aut_label': '3B', 'centralizer': '2.A', 'counter': 7, 'group_counter': 465, 'group_order': 472392, 'label': '3B', 'order': 3, 'powers': [7, 1], 'representative': 178848, 'size': 2}
id: 162871196
{'aut_label': '3C1', 'centralizer': '2.A', 'counter': 8, 'group_counter': 465, 'group_order': 472392, 'label': '3C1', 'order': 3, 'powers': [9, 1], 'representative': 44712, 'size': 2}
id: 162871207
{'aut_label': '3C1', 'centralizer': '2.A', 'counter': 9, 'group_counter': 465, 'group_order': 472392, 'label': '3C-1', 'order': 3, 'powers': [8, 1], 'representative': 31104, 'size': 2}
id: 162870692
{'aut_label': '3D', 'centralizer': '4.B', 'counter': 10, 'group_counter': 465, 'group_order': 472392, 'label': '3D', 'order': 3, 'powers': [10, 1], 'representative': 1944, 'size': 4}
id: 162870703
{'aut_label': '3E', 'centralizer': '4.C', 'counter': 11, 'group_counter': 465, 'group_order': 472392, 'label': '3E', 'order': 3, 'powers': [11, 1], 'representative': 4104, 'size': 4}
id: 162870714
{'aut_label': '3F1', 'centralizer': '4.B', 'counter': 12, 'group_counter': 465, 'group_order': 472392, 'label': '3F1', 'order': 3, 'powers': [13, 1], 'representative': 352080, 'size': 4}
id: 162870725
{'aut_label': '3F1', 'centralizer': '4.B', 'counter': 13, 'group_counter': 465, 'group_order': 472392, 'label': '3F-1', 'order': 3, 'powers': [12, 1], 'representative': 179280, 'size': 4}
id: 162870736
{'aut_label': '3G1', 'centralizer': '4.B', 'counter': 14, 'group_counter': 465, 'group_order': 472392, 'label': '3G1', 'order': 3, 'powers': [15, 1], 'representative': 330696, 'size': 4}
id: 162870747
{'aut_label': '3G1', 'centralizer': '4.B', 'counter': 15, 'group_counter': 465, 'group_order': 472392, 'label': '3G-1', 'order': 3, 'powers': [14, 1], 'representative': 165672, 'size': 4}
id: 162870758
{'aut_label': '3H1', 'centralizer': '4.B', 'counter': 16, 'group_counter': 465, 'group_order': 472392, 'label': '3H1', 'order': 3, 'powers': [17, 1], 'representative': 31320, 'size': 4}
id: 162870769
{'aut_label': '3H1', 'centralizer': '4.B', 'counter': 17, 'group_counter': 465, 'group_order': 472392, 'label': '3H-1', 'order': 3, 'powers': [16, 1], 'representative': 45144, 'size': 4}
id: 162870780
{'aut_label': '3I1', 'centralizer': '4.B', 'counter': 18, 'group_counter': 465, 'group_order': 472392, 'label': '3I1', 'order': 3, 'powers': [19, 1], 'representative': 204336, 'size': 4}
id: 162870791
{'aut_label': '3I1', 'centralizer': '4.B', 'counter': 19, 'group_counter': 465, 'group_order': 472392, 'label': '3I-1', 'order': 3, 'powers': [18, 1], 'representative': 338688, 'size': 4}
id: 162870803
{'aut_label': '3J1', 'centralizer': '4.C', 'counter': 20, 'group_counter': 465, 'group_order': 472392, 'label': '3J1', 'order': 3, 'powers': [21, 1], 'representative': 328968, 'size': 4}
id: 162870814
{'aut_label': '3J1', 'centralizer': '4.C', 'counter': 21, 'group_counter': 465, 'group_order': 472392, 'label': '3J-1', 'order': 3, 'powers': [20, 1], 'representative': 167400, 'size': 4}
id: 162870825
{'aut_label': '3K', 'centralizer': '8.a1', 'counter': 22, 'group_counter': 465, 'group_order': 472392, 'label': '3K', 'order': 3, 'powers': [22, 1], 'representative': 175176, 'size': 8}
id: 162870836
{'aut_label': '3L1', 'centralizer': '8.a1', 'counter': 23, 'group_counter': 465, 'group_order': 472392, 'label': '3L1', 'order': 3, 'powers': [24, 1], 'representative': 41040, 'size': 8}
id: 162870847
{'aut_label': '3L1', 'centralizer': '8.a1', 'counter': 24, 'group_counter': 465, 'group_order': 472392, 'label': '3L-1', 'order': 3, 'powers': [23, 1], 'representative': 29376, 'size': 8}
id: 162870858
{'aut_label': '3M', 'centralizer': '36.T', 'counter': 25, 'group_counter': 465, 'group_order': 472392, 'label': '3M', 'order': 3, 'powers': [25, 1], 'representative': 23760, 'size': 36}
id: 162870869
{'aut_label': '3N1', 'centralizer': '36.T', 'counter': 26, 'group_counter': 465, 'group_order': 472392, 'label': '3N1', 'order': 3, 'powers': [27, 1], 'representative': 346464, 'size': 36}
id: 162870880
{'aut_label': '3N1', 'centralizer': '36.T', 'counter': 27, 'group_counter': 465, 'group_order': 472392, 'label': '3N-1', 'order': 3, 'powers': [26, 1], 'representative': 202392, 'size': 36}
id: 162870891
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 28, 'group_counter': 465, 'group_order': 472392, 'label': '3O1', 'order': 3, 'powers': [29, 1], 'representative': 221428, 'size': 36}
id: 162870902
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 29, 'group_counter': 465, 'group_order': 472392, 'label': '3O-1', 'order': 3, 'powers': [28, 1], 'representative': 48848, 'size': 36}
id: 162870914
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 30, 'group_counter': 465, 'group_order': 472392, 'label': '3P1', 'order': 3, 'powers': [31, 1], 'representative': 170936, 'size': 36}
id: 162870925
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 31, 'group_counter': 465, 'group_order': 472392, 'label': '3P-1', 'order': 3, 'powers': [30, 1], 'representative': 75976, 'size': 36}
id: 162870936
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 32, 'group_counter': 465, 'group_order': 472392, 'label': '3Q1', 'order': 3, 'powers': [33, 1], 'representative': 396388, 'size': 36}
id: 162870947
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 33, 'group_counter': 465, 'group_order': 472392, 'label': '3Q-1', 'order': 3, 'powers': [32, 1], 'representative': 346280, 'size': 36}
id: 162870958
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 34, 'group_counter': 465, 'group_order': 472392, 'label': '3R1', 'order': 3, 'powers': [35, 1], 'representative': 97792, 'size': 36}
id: 162870969
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 35, 'group_counter': 465, 'group_order': 472392, 'label': '3R-1', 'order': 3, 'powers': [34, 1], 'representative': 168992, 'size': 36}
id: 162870980
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 36, 'group_counter': 465, 'group_order': 472392, 'label': '3S1', 'order': 3, 'powers': [37, 1], 'representative': 95068, 'size': 36}
id: 162870991
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 37, 'group_counter': 465, 'group_order': 472392, 'label': '3S-1', 'order': 3, 'powers': [36, 1], 'representative': 169376, 'size': 36}
id: 162871002
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 38, 'group_counter': 465, 'group_order': 472392, 'label': '3T1', 'order': 3, 'powers': [39, 1], 'representative': 349352, 'size': 36}
id: 162871013
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 39, 'group_counter': 465, 'group_order': 472392, 'label': '3T-1', 'order': 3, 'powers': [38, 1], 'representative': 375784, 'size': 36}
id: 162871025
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 40, 'group_counter': 465, 'group_order': 472392, 'label': '3U1', 'order': 3, 'powers': [41, 1], 'representative': 229204, 'size': 36}
id: 162871036
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 41, 'group_counter': 465, 'group_order': 472392, 'label': '3U-1', 'order': 3, 'powers': [40, 1], 'representative': 17744, 'size': 36}
id: 162871047
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 42, 'group_counter': 465, 'group_order': 472392, 'label': '3V1', 'order': 3, 'powers': [43, 1], 'representative': 390832, 'size': 36}
id: 162871058
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 43, 'group_counter': 465, 'group_order': 472392, 'label': '3V-1', 'order': 3, 'powers': [42, 1], 'representative': 334304, 'size': 36}
id: 162871069
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 44, 'group_counter': 465, 'group_order': 472392, 'label': '3W1', 'order': 3, 'powers': [45, 1], 'representative': 384076, 'size': 36}
id: 162871080
{'aut_label': '3O1', 'centralizer': '36.P', 'counter': 45, 'group_counter': 465, 'group_order': 472392, 'label': '3W-1', 'order': 3, 'powers': [44, 1], 'representative': 411080, 'size': 36}
id: 162871091
{'aut_label': '3X', 'centralizer': '72.W', 'counter': 46, 'group_counter': 465, 'group_order': 472392, 'label': '3X', 'order': 3, 'powers': [46, 1], 'representative': 17496, 'size': 72}
id: 162871102
{'aut_label': '3Y1', 'centralizer': '72.W', 'counter': 47, 'group_counter': 465, 'group_order': 472392, 'label': '3Y1', 'order': 3, 'powers': [48, 1], 'representative': 159408, 'size': 72}
id: 162871113
{'aut_label': '3Y1', 'centralizer': '72.W', 'counter': 48, 'group_counter': 465, 'group_order': 472392, 'label': '3Y-1', 'order': 3, 'powers': [47, 1], 'representative': 332424, 'size': 72}
id: 162871124
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 49, 'group_counter': 465, 'group_order': 472392, 'label': '3Z1', 'order': 3, 'powers': [50, 1], 'representative': 676, 'size': 72}
id: 162871136
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 50, 'group_counter': 465, 'group_order': 472392, 'label': '3Z-1', 'order': 3, 'powers': [49, 1], 'representative': 5864, 'size': 72}
id: 162871147
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 51, 'group_counter': 465, 'group_order': 472392, 'label': '3AA1', 'order': 3, 'powers': [52, 1], 'representative': 1324, 'size': 72}
id: 162871158
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 52, 'group_counter': 465, 'group_order': 472392, 'label': '3AA-1', 'order': 3, 'powers': [51, 1], 'representative': 7808, 'size': 72}
id: 162871167
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 53, 'group_counter': 465, 'group_order': 472392, 'label': '3AB1', 'order': 3, 'powers': [54, 1], 'representative': 1376, 'size': 72}
id: 162871168
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 54, 'group_counter': 465, 'group_order': 472392, 'label': '3AB-1', 'order': 3, 'powers': [53, 1], 'representative': 175636, 'size': 72}
id: 162871169
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 55, 'group_counter': 465, 'group_order': 472392, 'label': '3AC1', 'order': 3, 'powers': [56, 1], 'representative': 17528, 'size': 72}
id: 162871170
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 56, 'group_counter': 465, 'group_order': 472392, 'label': '3AC-1', 'order': 3, 'powers': [55, 1], 'representative': 176284, 'size': 72}
id: 162871171
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 57, 'group_counter': 465, 'group_order': 472392, 'label': '3AD1', 'order': 3, 'powers': [58, 1], 'representative': 314960, 'size': 72}
id: 162871172
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 58, 'group_counter': 465, 'group_order': 472392, 'label': '3AD-1', 'order': 3, 'powers': [57, 1], 'representative': 70072, 'size': 72}
id: 162871173
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 59, 'group_counter': 465, 'group_order': 472392, 'label': '3AE1', 'order': 3, 'powers': [60, 1], 'representative': 4564, 'size': 72}
id: 162871175
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 60, 'group_counter': 465, 'group_order': 472392, 'label': '3AE-1', 'order': 3, 'powers': [59, 1], 'representative': 9752, 'size': 72}
id: 162871176
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 61, 'group_counter': 465, 'group_order': 472392, 'label': '3AF1', 'order': 3, 'powers': [62, 1], 'representative': 158840, 'size': 72}
id: 162871177
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 62, 'group_counter': 465, 'group_order': 472392, 'label': '3AF-1', 'order': 3, 'powers': [61, 1], 'representative': 58408, 'size': 72}
id: 162871178
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 63, 'group_counter': 465, 'group_order': 472392, 'label': '3AG1', 'order': 3, 'powers': [64, 1], 'representative': 7208, 'size': 72}
id: 162871179
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 64, 'group_counter': 465, 'group_order': 472392, 'label': '3AG-1', 'order': 3, 'powers': [63, 1], 'representative': 41500, 'size': 72}
id: 162871180
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 65, 'group_counter': 465, 'group_order': 472392, 'label': '3AH1', 'order': 3, 'powers': [66, 1], 'representative': 54520, 'size': 72}
id: 162871181
{'aut_label': '3Z1', 'centralizer': '72.J', 'counter': 66, 'group_counter': 465, 'group_order': 472392, 'label': '3AH-1', 'order': 3, 'powers': [65, 1], 'representative': 158912, 'size': 72}
id: 162871182
{'aut_label': '3AI', 'centralizer': '324.FD', 'counter': 67, 'group_counter': 465, 'group_order': 472392, 'label': '3AI', 'order': 3, 'powers': [67, 1], 'representative': 139968, 'size': 324}
id: 162871183
{'aut_label': '3AJ1', 'centralizer': '324.FE', 'counter': 68, 'group_counter': 465, 'group_order': 472392, 'label': '3AJ1', 'order': 3, 'powers': [69, 1], 'representative': 310756, 'size': 324}
id: 162871184
{'aut_label': '3AJ1', 'centralizer': '324.FE', 'counter': 69, 'group_counter': 465, 'group_order': 472392, 'label': '3AJ-1', 'order': 3, 'powers': [68, 1], 'representative': 305516, 'size': 324}
id: 162871186
{'aut_label': '3AJ1', 'centralizer': '324.FE', 'counter': 70, 'group_counter': 465, 'group_order': 472392, 'label': '3AK1', 'order': 3, 'powers': [71, 1], 'representative': 49844, 'size': 324}
id: 162871187
{'aut_label': '3AJ1', 'centralizer': '324.FE', 'counter': 71, 'group_counter': 465, 'group_order': 472392, 'label': '3AK-1', 'order': 3, 'powers': [70, 1], 'representative': 14332, 'size': 324}
id: 162871188
{'aut_label': '3AJ1', 'centralizer': '324.FE', 'counter': 72, 'group_counter': 465, 'group_order': 472392, 'label': '3AL1', 'order': 3, 'powers': [73, 1], 'representative': 278932, 'size': 324}
id: 162871189
{'aut_label': '3AJ1', 'centralizer': '324.FE', 'counter': 73, 'group_counter': 465, 'group_order': 472392, 'label': '3AL-1', 'order': 3, 'powers': [72, 1], 'representative': 243812, 'size': 324}
id: 162871190
{'aut_label': '3AM', 'centralizer': None, 'counter': 74, 'group_counter': 465, 'group_order': 472392, 'label': '3AM', 'order': 3, 'powers': [74, 1], 'representative': 158196, 'size': 648}
id: 162871191
{'aut_label': '3AM', 'centralizer': None, 'counter': 75, 'group_counter': 465, 'group_order': 472392, 'label': '3AN', 'order': 3, 'powers': [75, 1], 'representative': 948, 'size': 648}
id: 162871192
{'aut_label': '3AM', 'centralizer': None, 'counter': 76, 'group_counter': 465, 'group_order': 472392, 'label': '3AO', 'order': 3, 'powers': [76, 1], 'representative': 12396, 'size': 648}
id: 162871193
{'aut_label': '3AP1', 'centralizer': None, 'counter': 77, 'group_counter': 465, 'group_order': 472392, 'label': '3AP1', 'order': 3, 'powers': [78, 1], 'representative': 732, 'size': 648}
id: 162871194
{'aut_label': '3AP1', 'centralizer': None, 'counter': 78, 'group_counter': 465, 'group_order': 472392, 'label': '3AP-1', 'order': 3, 'powers': [77, 1], 'representative': 35724, 'size': 648}
id: 162871195
{'aut_label': '3AP1', 'centralizer': None, 'counter': 79, 'group_counter': 465, 'group_order': 472392, 'label': '3AQ1', 'order': 3, 'powers': [80, 1], 'representative': 1380, 'size': 648}
id: 162871197
{'aut_label': '3AP1', 'centralizer': None, 'counter': 80, 'group_counter': 465, 'group_order': 472392, 'label': '3AQ-1', 'order': 3, 'powers': [79, 1], 'representative': 744, 'size': 648}
id: 162871198
{'aut_label': '3AR1', 'centralizer': None, 'counter': 81, 'group_counter': 465, 'group_order': 472392, 'label': '3AR1', 'order': 3, 'powers': [82, 1], 'representative': 32, 'size': 648}
id: 162871199
{'aut_label': '3AR1', 'centralizer': None, 'counter': 82, 'group_counter': 465, 'group_order': 472392, 'label': '3AR-1', 'order': 3, 'powers': [81, 1], 'representative': 160, 'size': 648}
id: 162871200
{'aut_label': '3AR1', 'centralizer': None, 'counter': 83, 'group_counter': 465, 'group_order': 472392, 'label': '3AS1', 'order': 3, 'powers': [84, 1], 'representative': 88, 'size': 648}
id: 162871201
{'aut_label': '3AR1', 'centralizer': None, 'counter': 84, 'group_counter': 465, 'group_order': 472392, 'label': '3AS-1', 'order': 3, 'powers': [83, 1], 'representative': 157496, 'size': 648}
id: 162871202
{'aut_label': '3AP1', 'centralizer': None, 'counter': 85, 'group_counter': 465, 'group_order': 472392, 'label': '3AT1', 'order': 3, 'powers': [86, 1], 'representative': 816, 'size': 648}
id: 162871203
{'aut_label': '3AP1', 'centralizer': None, 'counter': 86, 'group_counter': 465, 'group_order': 472392, 'label': '3AT-1', 'order': 3, 'powers': [85, 1], 'representative': 315660, 'size': 648}
id: 162871204
{'aut_label': '3AU1', 'centralizer': None, 'counter': 87, 'group_counter': 465, 'group_order': 472392, 'label': '3AU1', 'order': 3, 'powers': [88, 1], 'representative': 1372, 'size': 648}
id: 162871205
{'aut_label': '3AU1', 'centralizer': None, 'counter': 88, 'group_counter': 465, 'group_order': 472392, 'label': '3AU-1', 'order': 3, 'powers': [87, 1], 'representative': 157556, 'size': 648}
id: 162871206
{'aut_label': '3AU1', 'centralizer': None, 'counter': 89, 'group_counter': 465, 'group_order': 472392, 'label': '3AV1', 'order': 3, 'powers': [90, 1], 'representative': 92, 'size': 648}
id: 162871208
{'aut_label': '3AU1', 'centralizer': None, 'counter': 90, 'group_counter': 465, 'group_order': 472392, 'label': '3AV-1', 'order': 3, 'powers': [89, 1], 'representative': 315652, 'size': 648}
id: 162871209
{'aut_label': '3AR1', 'centralizer': None, 'counter': 91, 'group_counter': 465, 'group_order': 472392, 'label': '3AW1', 'order': 3, 'powers': [92, 1], 'representative': 157552, 'size': 648}
id: 162871210
{'aut_label': '3AR1', 'centralizer': None, 'counter': 92, 'group_counter': 465, 'group_order': 472392, 'label': '3AW-1', 'order': 3, 'powers': [91, 1], 'representative': 35024, 'size': 648}
id: 162871211
{'aut_label': '3AU1', 'centralizer': None, 'counter': 93, 'group_counter': 465, 'group_order': 472392, 'label': '3AX1', 'order': 3, 'powers': [94, 1], 'representative': 4612, 'size': 648}
id: 162871212
{'aut_label': '3AU1', 'centralizer': None, 'counter': 94, 'group_counter': 465, 'group_order': 472392, 'label': '3AX-1', 'order': 3, 'powers': [93, 1], 'representative': 740, 'size': 648}
id: 162871213
{'aut_label': '4A', 'centralizer': None, 'counter': 95, 'group_counter': 465, 'group_order': 472392, 'label': '4A', 'order': 4, 'powers': [4, 95], 'representative': 322221, 'size': 13122}
id: 162871214
{'aut_label': '6A1', 'centralizer': '54.F', 'counter': 96, 'group_counter': 465, 'group_order': 472392, 'label': '6A1', 'order': 6, 'powers': [8, 2], 'representative': 144558, 'size': 54}
id: 162871215
{'aut_label': '6A1', 'centralizer': '54.F', 'counter': 97, 'group_counter': 465, 'group_order': 472392, 'label': '6A-1', 'order': 6, 'powers': [9, 2], 'representative': 117342, 'size': 54}
id: 162871216
{'aut_label': '6B1', 'centralizer': '54.F', 'counter': 98, 'group_counter': 465, 'group_order': 472392, 'label': '6B1', 'order': 6, 'powers': [5, 2], 'representative': 459918, 'size': 54}
id: 162871217
{'aut_label': '6B1', 'centralizer': '54.F', 'counter': 99, 'group_counter': 465, 'group_order': 472392, 'label': '6B-1', 'order': 6, 'powers': [6, 2], 'representative': 312174, 'size': 54}
id: 162870693
{'aut_label': '6C1', 'centralizer': '54.F', 'counter': 100, 'group_counter': 465, 'group_order': 472392, 'label': '6C1', 'order': 6, 'powers': [7, 2], 'representative': 404676, 'size': 54}

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
Showing the first 100 of 153 matching records in this table.

id: 16174894
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '472392.rw', 'group_order': 472392, 'image': None, 'label': '472392.rw.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 16174959
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '472392.rw', 'group_order': 472392, 'image': None, 'label': '472392.rw.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 16174970
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '472392.rw', 'group_order': 472392, 'image': None, 'label': '472392.rw.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 16174981
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '472392.rw', 'group_order': 472392, 'image': None, 'label': '472392.rw.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 16174992
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id: 16174895
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id: 16174917
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id: 16174928
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id: 16174939
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id: 16174950
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id: 16174955
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id: 16174956
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id: 16174957
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id: 16174958
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id: 16174962
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id: 16174969
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id: 16174971
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id: 16174972
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id: 16174986
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id: 16174993
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id: 16175000
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id: 16175001
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id: 16175005
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id: 16175006
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id: 16175007
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id: 16175009
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id: 16175011
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id: 16175012
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id: 16174977
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id: 16174978
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id: 16174907
{'cdim': 36, 'counter': 110, 'faithful': False, 'group': '472392.rw', 'group_order': 472392, 'image': None, 'label': '472392.rw.36d', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 12, 0, -36, -36, 72, -36, -36, -36, 18, -36, -36, 18, 18, 18, 18, 18, 18, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 18, 18, 18, 18, -18, -18, 0, 0, 0, 0, 18, 18, -18, -18, -18, -18, 0, 0, 0, -9, -9, 0, 0, 0, 0, -9, -9, 9, 9, 9, 9, -9, -9, 9, 9, 0, 0, 0, 3, 3, 3, 3, -6, -6, 6, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, -3, -3, 3, 3, 3, 3, 0, 0, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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}
id: 16174908
{'cdim': 36, 'counter': 111, 'faithful': False, 'group': '472392.rw', 'group_order': 472392, 'image': None, 'label': '472392.rw.36e', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 12, 0, -36, -36, 72, -36, -36, -36, 18, -36, -36, 18, 18, 18, 18, 18, 18, -9, -9, 18, -9, -9, 0, 0, 0, 18, 18, -18, -18, -18, -18, 0, 0, 18, 18, 18, 18, -18, -18, 0, 0, 0, 0, 0, 0, 0, 9, 9, -9, -9, -9, -9, 9, 9, 0, 0, 0, 0, 9, 9, 0, 0, -9, -9, 0, 3, 3, -6, -6, 3, 3, 6, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, -3, -3, -6, -6, 3, 3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 472392.rw 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
Showing the first 100 of 806 matching records in this table.

id: 217181260
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 472392, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '472392.rw.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['R', 'L0', 'D0', 'C0'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '472392.rw', 'subgroup_hash': 4458908981959553522, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
id: 217181371
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 236196, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.2.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 340208659364747194, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3^4.C_2^2', 'supersolvable': True, 'sylow': 0}
id: 217181482
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 236196, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.lh', 'subgroup_hash': 8198807337538431408, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
id: 217181593
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 236196, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.2.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.lt', 'subgroup_hash': 8205912189180883211, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
id: 217181704
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 157464, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.3.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.qx', 'subgroup_hash': 1425006708033936817, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
id: 217181815
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 78732, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.3.B', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', '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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.sb', 'subgroup_hash': 889702245471581537, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^4:D_9^2.C_6', 'supersolvable': False, 'sylow': 0}
id: 217181926
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 118098, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3518229174562669243, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
id: 217182037
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1', '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': None, 'subgroup_hash': 7894505538339019415, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^3.C_3^4.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
id: 217182055
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 4514826845252250347, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
id: 217181261
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id: 217181272
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id: 217181283
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id: 217181294
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id: 217181305
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id: 217181316
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id: 217181327
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 39366, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.6.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.kg', 'subgroup_hash': 8906847388816749675, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.(C_3\\times S_3^2)', 'supersolvable': True, 'sylow': 0}
id: 217181338
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id: 217181349
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 39366, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.6.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.li', 'subgroup_hash': 4094729405608444377, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^4.C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 217181360
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 59049, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '472392.rw.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 56042109095087524, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 3}
id: 217181372
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6561, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.9.A', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', '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': 9, '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': '52488.oz', 'subgroup_hash': 3894498303307350474, 'subgroup_order': 52488, 'subgroup_tex': '(C_3:S_3:C_9)\\wr C_2', 'supersolvable': False, 'sylow': 0}
id: 217181383
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 26244, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.9.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', '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': 9, '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': '52488.md', 'subgroup_hash': 9063690763117432479, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
id: 217181394
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 39366, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1617664516712860841, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181405
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 39366, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1617664516712860841, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181416
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7538404885108620235, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
id: 217181427
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 567972047900213034, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^3.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181438
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id: 217181449
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id: 217181460
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id: 217181471
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id: 217181483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1206738856853824893, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^3.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181494
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4335326722565386717, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^3.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181505
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4335326722565386717, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^3.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181516
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4335326722565386717, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^3.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181527
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7999269442015727279, 'subgroup_order': 39366, 'subgroup_tex': 'C_3.C_3^5.\\He_3.C_2', 'supersolvable': True, 'sylow': 0}
id: 217181538
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4144341226551984197, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^4.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181549
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4144341226551984197, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^4.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181560
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', '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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5955212944316845953, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181571
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', '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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7877293562513805723, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181582
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', '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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7877293562513805723, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181594
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 6561, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', '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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1003861659929806046, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^3.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181605
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 6561, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', '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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2465730706555934874, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
id: 217181616
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 13122, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.12.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', '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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1479708702571070463, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
id: 217181627
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 26244, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7803675823749077841, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^4.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 217181638
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 6561, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', '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': 18, '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': None, 'subgroup_hash': 2824199659284287672, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.C_6^2', 'supersolvable': True, 'sylow': 0}
id: 217181649
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': None, 'subgroup_hash': 8451122763968975546, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^4.C_3^2.C_6^2', 'supersolvable': True, 'sylow': 0}
id: 217181660
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': None, 'subgroup_hash': 379166065284961575, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^3.C_3^3.C_6^2', 'supersolvable': True, 'sylow': 0}
id: 217181671
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': None, 'subgroup_hash': 6264930220505848733, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^3.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
id: 217181682
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': None, 'subgroup_hash': 57573705632996409, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^3.C_3^4.C_6.C_2', 'supersolvable': True, 'sylow': 0}
id: 217181693
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 2187, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': None, 'subgroup_hash': 5228442540036272905, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^3.C_3^4.C_6.C_2', 'supersolvable': True, 'sylow': 0}
id: 217181705
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 2187, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': None, 'subgroup_hash': 5228442540036272905, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^3.C_3^4.C_6.C_2', 'supersolvable': True, 'sylow': 0}
id: 217181716
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2187, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '26244.kn', 'subgroup_hash': 6243240361113522248, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
id: 217181727
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6561, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '26244.ki', 'subgroup_hash': 6569551656027437563, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^4:(C_9\\times D_{18})', 'supersolvable': True, 'sylow': 0}
id: 217181738
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 13122, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '26244.iw', 'subgroup_hash': 973772430782429590, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^4:D_9^2', 'supersolvable': True, 'sylow': 0}
id: 217181749
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2187, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '26244.jj', 'subgroup_hash': 5744338894333675537, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.S_3^2', 'supersolvable': True, 'sylow': 0}
id: 217181760
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6561, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, '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': '26244.kx', 'subgroup_hash': 5485875702808977145, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^3.C_3^4.C_{12}', 'supersolvable': False, 'sylow': 0}
id: 217181771
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 13122, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.18.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '26244.jv', 'subgroup_hash': 8337380404941439409, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^4:(C_9^2:C_4)', 'supersolvable': False, 'sylow': 0}
id: 217181782
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 19683, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3228434382783733641, 'subgroup_order': 19683, 'subgroup_tex': 'C_3^6.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 217181793
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 19683, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3228434382783733641, 'subgroup_order': 19683, 'subgroup_tex': 'C_3^6.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 217181804
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 729, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 958988385768509243, 'subgroup_order': 19683, 'subgroup_tex': 'C_3^6.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 217181816
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id: 217181827
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id: 217181838
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id: 217181849
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id: 217181860
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id: 217181871
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id: 217181882
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id: 217181893
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id: 217181904
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id: 217181915
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id: 217181927
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id: 217181938
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id: 217181949
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id: 217181960
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id: 217181971
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id: 217181982
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id: 217181993
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id: 217182004
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id: 217182015
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id: 217182026
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, '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': None, 'subgroup_hash': 8142219371162629713, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182038
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, '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': None, 'subgroup_hash': 2607453797263673998, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^5.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
id: 217182046
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, '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': None, 'subgroup_hash': 8142219371162629713, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182047
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, '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': None, 'subgroup_hash': 8142219371162629713, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182048
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, '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': None, 'subgroup_hash': 6964505667827318056, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^2:C_9.\\He_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182049
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': None, 'subgroup_hash': 1054292346750071237, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182050
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': None, 'subgroup_hash': 1054292346750071237, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^2:C_9.C_9.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182051
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', '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': 36, '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': None, 'subgroup_hash': 8692926064504016271, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
id: 217182052
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', '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': 36, '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': None, 'subgroup_hash': 1000414473145922575, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182053
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', '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': 36, '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': None, 'subgroup_hash': 1000414473145922575, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182054
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', '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': 36, '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': None, 'subgroup_hash': 4632797135427698692, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^2:C_9.\\He_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182056
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', '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': 36, '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': None, 'subgroup_hash': 8692926064504016271, 'subgroup_order': 13122, 'subgroup_tex': 'C_3\\times C_3^3.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
id: 217182057
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', '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': 36, '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': None, 'subgroup_hash': 6964505667827318056, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^2:C_9.\\He_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182058
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', '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': 36, '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': None, 'subgroup_hash': 6964505667827318056, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^2:C_9.\\He_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182059
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', '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': 36, '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': None, 'subgroup_hash': 2755925957208422888, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^2.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182060
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', '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': 36, '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': None, 'subgroup_hash': 5722751424534036200, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182061
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', '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': 36, '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': None, 'subgroup_hash': 5722751424534036200, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182062
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1', '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': 36, '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': None, 'subgroup_hash': 5722751424534036200, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182063
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1', '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': 36, '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': None, 'subgroup_hash': 2755925957208422888, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^2.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182064
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1', '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': 36, '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': None, 'subgroup_hash': 7994062853637474268, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
id: 217182065
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1', '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': 36, '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': None, 'subgroup_hash': 2563756802977770183, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 217181262
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.rw', 'ambient_counter': 465, 'ambient_order': 472392, 'ambient_tex': 'C_3^6.C_3\\wr D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.rw.36.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1', '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': 36, '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': None, 'subgroup_hash': 4616866316041270115, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}

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

gps_subgroup_data • Show schema
Showing the first 100 of 806 matching records in this table.

id: 217181260
{'ambient': '472392.rw', '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': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [39, 2330, 7, 238], 'generators': [425541, 324, 338256, 112554, 208656, 164448, 2160, 112556, 174960, 351864, 134580, 15768, 62640], 'label': '472392.rw.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': None, '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': None}
id: 217181261
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.A', 'coset_action_label': None, 'count': 1, 'diagramx': [35, 2081, 119, 2958], 'generators': [324, 1944, 4536, 385344, 163296, 112554, 164448, 2160, 15984, 174960, 112556], 'label': '472392.rw.6.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181262
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1032, -1, 1143, -1], 'generators': [189345, 167400, 397812, 223560, 113276, 174960, 163296, 206064, 23544], 'label': '472392.rw.36.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.M', 'old_label': '36.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BD', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181263
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1507, -1, 1303, -1], 'generators': [189345, 167400, 397812, 62640, 113996, 174960, 163296, 42768, 23544], 'label': '472392.rw.36.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.M', 'old_label': '36.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BE', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181264
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1095, -1, 1164, -1], 'generators': [189345, 351864, 159852, 225504, 113276, 40824, 2160, 174960, 23544], 'label': '472392.rw.36.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '36.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BF', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181265
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1063, -1, 1154, -1], 'generators': [189345, 165240, 34632, 400680, 286220, 174960, 4104, 338256, 23544], 'label': '472392.rw.36.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '36.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BG', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181266
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 6, 'diagramx': [437, -1, 942, -1], 'generators': [189345, 165240, 329904, 249048, 112556, 174960, 4104, 338256, 23544], 'label': '472392.rw.36.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '36.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BH', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181267
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1604, -1, 1336, -1], 'generators': [189345, 167400, 397812, 408672, 112556, 174960, 163296, 206064, 23544], 'label': '472392.rw.36.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.M', 'old_label': '36.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BI', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181268
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1570, -1, 1325, -1], 'generators': [189345, 167400, 397812, 62640, 165960, 174960, 163296, 351864, 23544], 'label': '472392.rw.36.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.M', 'old_label': '36.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BJ', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181269
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 6, 'diagramx': [469, -1, 953, -1], 'generators': [189345, 351864, 159852, 222048, 165960, 338256, 2160, 174960, 23544], 'label': '472392.rw.36.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '36.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BK', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181270
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [540, -1, 977, -1], 'generators': [189345, 351864, 159852, 223560, 112556, 338256, 2160, 174960, 23544], 'label': '472392.rw.36.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '36.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BL', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181271
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.B', 'coset_action_label': None, 'count': 6, 'diagramx': [503, -1, 964, -1], 'generators': [189345, 165240, 329904, 223560, 331128, 174960, 4104, 338256, 23544], 'label': '472392.rw.36.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '36.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BM', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181272
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.B', 'coset_action_label': None, 'count': 1, 'diagramx': [71, 4574, 131, 3402], 'generators': [324, 1944, 4536, 369792, 338256, 112554, 164448, 2160, 25488, 174960, 237180], 'label': '472392.rw.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181273
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 2, 'diagramx': [1235, -1, 1212, -1], 'generators': [189345, 351864, 91584, 338256, 159852, 13824, 4104, 174960, 329904], 'label': '472392.rw.36.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '36.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BN', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181274
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 18, 'diagramx': [740, -1, 1044, -1], 'generators': [112554, 338256, 208656, 392688, 112556, 174960, 1944, 2160, 260724], 'label': '472392.rw.36.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '36.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BO', 'subgroup_fusion': None, 'weyl_group': '972.444'}
id: 217181275
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 36, 'diagramx': [860, -1, 1085, -1], 'generators': [112554, 338256, 162216, 393120, 112556, 174960, 1944, 216, 260724], 'label': '472392.rw.36.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BP', 'old_label': '36.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BP', 'subgroup_fusion': None, 'weyl_group': '1458.1150'}
id: 217181276
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 9, 'diagramx': [1404, -1, 1269, -1], 'generators': [112554, 1944, 174960, 54432, 112556, 338256, 216, 25488, 237180], 'label': '472392.rw.36.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '36.bq1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BQ', 'subgroup_fusion': None, 'weyl_group': '5832.cg'}
id: 217181277
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 18, 'diagramx': [403, -1, 931, -1], 'generators': [112554, 338256, 208656, 390744, 250376, 164448, 1944, 2160, 174960], 'label': '472392.rw.36.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '36.br1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BR', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181278
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 36, 'diagramx': [575, -1, 988, -1], 'generators': [112554, 174960, 390744, 2160, 250376, 162216, 40824, 31104, 164448], 'label': '472392.rw.36.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BS', 'old_label': '36.bs1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BS', 'subgroup_fusion': None, 'weyl_group': '1458.1075'}
id: 217181279
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 6, 'diagramx': [141, -1, 842, -1], 'generators': [112554, 338256, 390744, 25488, 244328, 208656, 1944, 2160, 174960], 'label': '472392.rw.36.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '36.bt1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BT', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181280
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 6, 'diagramx': [675, -1, 1022, -1], 'generators': [112554, 338256, 23544, 174960, 112556, 385344, 165240, 2160, 164448], 'label': '472392.rw.36.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '36.bu1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BU', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181281
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 6, 'diagramx': [706, -1, 1033, -1], 'generators': [112554, 338256, 25488, 174960, 237180, 369792, 351864, 2160, 164448], 'label': '472392.rw.36.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '36.bv1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BV', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181282
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 6, 'diagramx': [970, -1, 1122, -1], 'generators': [112554, 338256, 54432, 25704, 178640, 208656, 1944, 216, 174960], 'label': '472392.rw.36.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '36.bw1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BW', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181283
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.C', 'coset_action_label': None, 'count': 1, 'diagramx': [278, 9035, 201, 4196], 'generators': [189345, 351864, 339120, 222048, 338256, 112554, 164448, 2160, 37152, 174960, 159852], 'label': '472392.rw.6.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181284
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1377, -1, 1259, -1], 'generators': [112554, 338256, 25488, 174960, 244328, 404352, 31104, 2160, 164448], 'label': '472392.rw.36.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.T', 'old_label': '36.bx1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BX', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181285
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 6, 'diagramx': [369, -1, 919, -1], 'generators': [112554, 338256, 392688, 23544, 112556, 208656, 1944, 216, 174960], 'label': '472392.rw.36.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '36.by1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BY', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181286
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '36.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 6, 'diagramx': [338, -1, 909, -1], 'generators': [112554, 338256, 392688, 25488, 237180, 208656, 1944, 216, 174960], 'label': '472392.rw.36.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '36.bz1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BZ', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181287
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 54, 'diagramx': [28, -1, 1401, -1], 'generators': [324, 1944, 163296, 174960, 112554, 105204, 2160, 54432, 112556], 'label': '472392.rw.54.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.A', 'old_label': '54.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.A', 'subgroup_fusion': None, 'weyl_group': '324.116'}
id: 217181288
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 54, 'diagramx': [600, -1, 1594, -1], 'generators': [54756, 1944, 40824, 208656, 112554, 174960, 216, 25704, 178640], 'label': '472392.rw.54.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.B', 'old_label': '54.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.B', 'subgroup_fusion': None, 'weyl_group': '972.424'}
id: 217181289
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 18, 'diagramx': [54, -1, 1409, -1], 'generators': [324, 1944, 338256, 54432, 112554, 174960, 2160, 25488, 244328], 'label': '472392.rw.54.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '54.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181290
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 9, 'diagramx': [79, -1, 1418, -1], 'generators': [324, 1944, 163296, 54432, 112554, 174960, 216, 23544, 112556], 'label': '472392.rw.54.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '54.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.D', 'subgroup_fusion': None, 'weyl_group': '5832.cg'}
id: 217181291
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 9, 'diagramx': [113, -1, 1429, -1], 'generators': [324, 1944, 174960, 54432, 112554, 338256, 216, 25488, 237180], 'label': '472392.rw.54.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '54.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.E', 'subgroup_fusion': None, 'weyl_group': '5832.cg'}
id: 217181292
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '52488.A', 'coset_action_label': None, 'count': 54, 'diagramx': [726, -1, 1636, -1], 'generators': [324, 338256, 330480, 2592, 112554, 260724, 1944, 392688, 112556], 'label': '472392.rw.54.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.F', 'old_label': '54.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.F', 'subgroup_fusion': None, 'weyl_group': '162.15'}
id: 217181293
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '52488.A', 'coset_action_label': None, 'count': 54, 'diagramx': [213, -1, 1463, -1], 'generators': [324, 338256, 2592, 390744, 112554, 174960, 1944, 25488, 92696], 'label': '472392.rw.54.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.G', 'old_label': '54.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.G', 'subgroup_fusion': None, 'weyl_group': '972.444'}
id: 217181294
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.D', 'coset_action_label': None, 'count': 1, 'diagramx': [105, 6870, 142, 3810], 'generators': [425541, 351864, 208656, 62640, 338256, 112554, 164448, 2160, 15768, 174960, 134580], 'label': '472392.rw.6.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.D', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181295
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 18, 'diagramx': [248, -1, 1475, -1], 'generators': [324, 338256, 4536, 390744, 112554, 174960, 1944, 2160, 250376], 'label': '472392.rw.54.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '54.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.H', 'subgroup_fusion': None, 'weyl_group': '972.444'}
id: 217181296
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 18, 'diagramx': [641, -1, 1608, -1], 'generators': [324, 338256, 4536, 54432, 112554, 174960, 1944, 2160, 172592], 'label': '472392.rw.54.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '54.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.I', 'subgroup_fusion': None, 'weyl_group': '972.444'}
id: 217181297
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 18, 'diagramx': [390, -1, 1523, -1], 'generators': [324, 338256, 4536, 392688, 112554, 174960, 1944, 2160, 112556], 'label': '472392.rw.54.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '54.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.J', 'subgroup_fusion': None, 'weyl_group': '972.444'}
id: 217181298
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 18, 'diagramx': [348, -1, 1509, -1], 'generators': [324, 338256, 4536, 392688, 112554, 174960, 1944, 2160, 260724], 'label': '472392.rw.54.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '54.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.K', 'subgroup_fusion': None, 'weyl_group': '972.444'}
id: 217181299
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 18, 'diagramx': [497, -1, 1559, -1], 'generators': [324, 338256, 4536, 54432, 112554, 164448, 1944, 2160, 174960], 'label': '472392.rw.54.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '54.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.L', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181300
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 6, 'diagramx': [462, -1, 1547, -1], 'generators': [324, 338256, 54432, 23544, 112554, 4536, 1944, 2160, 174960], 'label': '472392.rw.54.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '54.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.M', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181301
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': None, 'contains': None, 'core': '52488.B', 'coset_action_label': None, 'count': 54, 'diagramx': [837, -1, 1674, -1], 'generators': [324, 338256, 2592, 390744, 112554, 168120, 1944, 2160, 411728], 'label': '472392.rw.54.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '54.n1', 'projective_image': '472392.rw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.N', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181302
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': None, 'contains': None, 'core': '52488.B', 'coset_action_label': None, 'count': 18, 'diagramx': [802, -1, 1662, -1], 'generators': [324, 338256, 390744, 23544, 112554, 2592, 1944, 2160, 215168], 'label': '472392.rw.54.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '54.o1', 'projective_image': '472392.rw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.O', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181303
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 27, 'diagramx': [528, -1, 1569, -1], 'generators': [189345, 174960, 103032, 23544, 112554, 163296, 1944, 4104, 112556], 'label': '472392.rw.54.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.A', 'old_label': '54.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.P', 'subgroup_fusion': None, 'weyl_group': '5832.ks'}
id: 217181304
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 54, 'diagramx': [560, -1, 1580, -1], 'generators': [123249, 165240, 385344, 338256, 112554, 164448, 2160, 174960, 112556], 'label': '472392.rw.54.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.Q', 'old_label': '54.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.Q', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181305
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [175, -1, 166, -1], 'generators': [324, 216, 174960, 4536, 1944, 112554, 237180, 25488, 392688, 338256, 112556], 'label': '472392.rw.6.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '6.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.E', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181306
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 54, 'diagramx': [683, -1, 1622, -1], 'generators': [189345, 351864, 381252, 103032, 112554, 338256, 2160, 174960, 112556], 'label': '472392.rw.54.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.R', 'old_label': '54.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.R', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181307
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 18, 'diagramx': [427, -1, 1536, -1], 'generators': [189345, 338256, 23544, 174960, 112554, 103032, 351864, 2160, 164448], 'label': '472392.rw.54.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.I', 'old_label': '54.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.S', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181308
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 54, 'diagramx': [767, -1, 1650, -1], 'generators': [189345, 174960, 103032, 2160, 112554, 339120, 338256, 1944, 164448], 'label': '472392.rw.54.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.T', 'old_label': '54.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.T', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181309
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 9, 'diagramx': [178, -1, 1451, -1], 'generators': [189345, 174960, 103464, 23544, 112554, 159852, 351864, 2160, 338256], 'label': '472392.rw.54.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '54.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.U', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181310
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 54, 'diagramx': [310, -1, 1496, -1], 'generators': [189345, 351864, 164448, 174960, 112554, 159852, 2160, 222048, 338256], 'label': '472392.rw.54.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.V', 'old_label': '54.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.V', 'subgroup_fusion': None, 'weyl_group': '2916.jo'}
id: 217181311
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 27, 'diagramx': [147, -1, 1441, -1], 'generators': [425541, 174960, 101520, 324648, 112556, 338256, 351864, 4104, 112554], 'label': '472392.rw.54.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.A', 'old_label': '54.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.W', 'subgroup_fusion': None, 'weyl_group': '5832.ks'}
id: 217181312
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '54.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 9, 'diagramx': [279, -1, 1486, -1], 'generators': [425541, 174960, 254880, 198288, 338256, 134580, 351864, 4104, 112554], 'label': '472392.rw.54.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '54.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.X', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181313
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 1, 'diagramx': [439, 1608, 1823, 7021], 'generators': [112556, 237180, 392688, 23544], 'label': '472392.rw.72.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.A', 'subgroup_fusion': None, 'weyl_group': '5832.cg'}
id: 217181314
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.B', 'coset_action_label': None, 'count': 1, 'diagramx': [465, 3367, 1831, 7334], 'generators': [165960, 331128, 392688, 23544], 'label': '472392.rw.72.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.B', 'subgroup_fusion': None, 'weyl_group': '5832.cg'}
id: 217181315
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 24, 'diagramx': [696, -1, 1909, -1], 'generators': [113276, 372756, 337176, 174960], 'label': '472392.rw.72.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '72.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.C', 'subgroup_fusion': None, 'weyl_group': '243.62'}
id: 217181316
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '18.A', 'coset_action_label': None, 'count': 2, 'diagramx': [139, -1, 154, -1], 'generators': [324, 1944, 4536, 404352, 338256, 112554, 164448, 2160, 25488, 174960, 244328], 'label': '472392.rw.6.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '6.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.F', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181317
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 24, 'diagramx': [736, -1, 1923, -1], 'generators': [142220, 372756, 331128, 174960], 'label': '472392.rw.72.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '72.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.D', 'subgroup_fusion': None, 'weyl_group': '486.222'}
id: 217181318
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 24, 'diagramx': [181, -1, 1736, -1], 'generators': [112556, 237180, 337176], 'label': '472392.rw.72.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.I', 'old_label': '72.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.E', 'subgroup_fusion': None, 'weyl_group': '243.62'}
id: 217181319
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 24, 'diagramx': [156, -1, 1727, -1], 'generators': [244328, 165960, 337176], 'label': '472392.rw.72.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.H', 'old_label': '72.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.F', 'subgroup_fusion': None, 'weyl_group': '243.62'}
id: 217181320
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 48, 'diagramx': [577, -1, 1869, -1], 'generators': [142220, 372756, 337176, 174960], 'label': '472392.rw.72.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.J', 'old_label': '72.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.G', 'subgroup_fusion': None, 'weyl_group': '243.62'}
id: 217181321
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 6, 'diagramx': [341, -1, 1790, -1], 'generators': [250376, 165960, 331128, 174960], 'label': '472392.rw.72.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.H', 'subgroup_fusion': None, 'weyl_group': '324.116'}
id: 217181322
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 6, 'diagramx': [381, -1, 1803, -1], 'generators': [135452, 237180, 331128, 2160], 'label': '472392.rw.72.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '72.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.I', 'subgroup_fusion': None, 'weyl_group': '324.116'}
id: 217181323
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 12, 'diagramx': [998, -1, 2012, -1], 'generators': [113276, 174960, 372756, 331128, 2160], 'label': '472392.rw.72.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '72.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.J', 'subgroup_fusion': None, 'weyl_group': '162.34'}
id: 217181324
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 12, 'diagramx': [913, -1, 1983, -1], 'generators': [112556, 237180, 331128], 'label': '472392.rw.72.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '72.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.K', 'subgroup_fusion': None, 'weyl_group': '486.222'}
id: 217181325
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 12, 'diagramx': [938, -1, 1991, -1], 'generators': [250376, 165960, 337176], 'label': '472392.rw.72.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '72.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.L', 'subgroup_fusion': None, 'weyl_group': '486.242'}
id: 217181326
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 12, 'diagramx': [888, -1, 1974, -1], 'generators': [135452, 237180, 337176], 'label': '472392.rw.72.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '72.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.M', 'subgroup_fusion': None, 'weyl_group': '486.229'}
id: 217181327
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': [312, -1, 212, -1], 'generators': [189345, 1944, 339120, 385344, 163296, 112554, 164448, 2160, 15984, 174960, 112556], 'label': '472392.rw.6.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.B', 'old_label': '6.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.G', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181328
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 12, 'diagramx': [964, -1, 2000, -1], 'generators': [244328, 165960, 331128], 'label': '472392.rw.72.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.G', 'old_label': '72.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.N', 'subgroup_fusion': None, 'weyl_group': '486.222'}
id: 217181329
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 8, 'diagramx': [656, -1, 1896, -1], 'generators': [113996, 246252, 392688, 174960], 'label': '472392.rw.72.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.O', 'subgroup_fusion': None, 'weyl_group': '729.453'}
id: 217181330
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 8, 'diagramx': [617, -1, 1883, -1], 'generators': [465716, 372756, 392688, 174960], 'label': '472392.rw.72.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.P', 'subgroup_fusion': None, 'weyl_group': '729.453'}
id: 217181331
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [498, -1, 1842, -1], 'generators': [465716, 174960, 246252, 392688, 23544], 'label': '472392.rw.72.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '72.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Q', 'subgroup_fusion': None, 'weyl_group': '1458.1573'}
id: 217181332
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [537, -1, 1856, -1], 'generators': [338768, 174960, 331128, 392688, 23544], 'label': '472392.rw.72.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '72.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.R', 'subgroup_fusion': None, 'weyl_group': '1458.1573'}
id: 217181333
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 4, 'diagramx': [308, -1, 1779, -1], 'generators': [112556, 246252, 23544], 'label': '472392.rw.72.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '72.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.S', 'subgroup_fusion': None, 'weyl_group': '1458.1573'}
id: 217181334
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 4, 'diagramx': [283, -1, 1770, -1], 'generators': [286220, 237180, 23544], 'label': '472392.rw.72.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '72.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.T', 'subgroup_fusion': None, 'weyl_group': '1458.1573'}
id: 217181335
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 8, 'diagramx': [257, -1, 1761, -1], 'generators': [213872, 165960, 23544], 'label': '472392.rw.72.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.U', 'subgroup_fusion': None, 'weyl_group': '729.453'}
id: 217181336
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1273, -1, 2105, -1], 'generators': [286940, 174960, 338256, 372756, 392688, 23544], 'label': '472392.rw.72.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '72.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.V', 'subgroup_fusion': None, 'weyl_group': '1458.1572'}
id: 217181337
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 2, 'diagramx': [1047, -1, 2028, -1], 'generators': [244328, 174960, 331128, 23544, 2160], 'label': '472392.rw.72.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '72.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.W', 'subgroup_fusion': None, 'weyl_group': '972.780'}
id: 217181338
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [244, -1, 189, -1], 'generators': [189345, 174960, 164448, 190512, 2160, 112554, 159852, 338256, 222048, 351864, 112556], 'label': '472392.rw.6.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '6.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.H', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181339
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 8, 'diagramx': [775, -1, 1936, -1], 'generators': [113276, 372756, 23544, 174960], 'label': '472392.rw.72.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.X', 'subgroup_fusion': None, 'weyl_group': '729.453'}
id: 217181340
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1308, -1, 2116, -1], 'generators': [461324, 372756, 23544], 'label': '472392.rw.72.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '72.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Y', 'subgroup_fusion': None, 'weyl_group': '1458.1572'}
id: 217181341
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 4, 'diagramx': [1213, -1, 2084, -1], 'generators': [113276, 237180, 23544], 'label': '472392.rw.72.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '72.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Z', 'subgroup_fusion': None, 'weyl_group': '1458.1572'}
id: 217181342
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 8, 'diagramx': [1112, -1, 2050, -1], 'generators': [113276, 246252, 23544], 'label': '472392.rw.72.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BA', 'subgroup_fusion': None, 'weyl_group': '729.453'}
id: 217181343
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1239, -1, 2093, -1], 'generators': [286220, 165960, 23544], 'label': '472392.rw.72.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '72.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BB', 'subgroup_fusion': None, 'weyl_group': '1458.1572'}
id: 217181344
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [855, -1, 1963, -1], 'generators': [113276, 331128, 23544, 174960], 'label': '472392.rw.72.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '72.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BC', 'subgroup_fusion': None, 'weyl_group': '1458.1573'}
id: 217181345
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 2, 'diagramx': [1359, -1, 2133, -1], 'generators': [112556, 165960, 23544], 'label': '472392.rw.72.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '72.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BD', 'subgroup_fusion': None, 'weyl_group': '2916.ea'}
id: 217181346
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1162, -1, 2067, -1], 'generators': [112556, 372756, 23544], 'label': '472392.rw.72.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '72.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BE', 'subgroup_fusion': None, 'weyl_group': '1458.1572'}
id: 217181347
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1188, -1, 2076, -1], 'generators': [399324, 165960, 23544], 'label': '472392.rw.72.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '72.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BF', 'subgroup_fusion': None, 'weyl_group': '1458.1572'}
id: 217181348
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 8, 'diagramx': [1137, -1, 2058, -1], 'generators': [286220, 372756, 23544], 'label': '472392.rw.72.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BG', 'subgroup_fusion': None, 'weyl_group': '729.453'}
id: 217181349
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '6.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': [209, -1, 178, -1], 'generators': [425541, 1944, 208656, 385344, 163296, 112556, 164448, 2160, 15984, 174960, 112554], 'label': '472392.rw.6.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.B', 'old_label': '6.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.I', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181350
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [815, -1, 1950, -1], 'generators': [372756, 331128, 23544, 174960], 'label': '472392.rw.72.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '72.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BH', 'subgroup_fusion': None, 'weyl_group': '1458.1573'}
id: 217181351
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 2, 'diagramx': [1333, -1, 2125, -1], 'generators': [237180, 165960, 23544], 'label': '472392.rw.72.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '72.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BI', 'subgroup_fusion': None, 'weyl_group': '2916.ea'}
id: 217181352
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 2, 'diagramx': [413, -1, 1814, -1], 'generators': [178640, 331128, 392688, 23544], 'label': '472392.rw.72.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '72.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BJ', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181353
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [79, -1, 1701, -1], 'generators': [286220, 246252, 23544], 'label': '472392.rw.72.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '72.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BK', 'subgroup_fusion': None, 'weyl_group': '1458.1573'}
id: 217181354
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [54, -1, 1693, -1], 'generators': [244328, 165960, 23544], 'label': '472392.rw.72.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.A', 'old_label': '72.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BL', 'subgroup_fusion': None, 'weyl_group': '1458.1577'}
id: 217181355
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 2, 'diagramx': [105, -1, 1710, -1], 'generators': [112556, 331128, 23544], 'label': '472392.rw.72.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '72.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BM', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181356
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.B', 'coset_action_label': None, 'count': 2, 'diagramx': [130, -1, 1719, -1], 'generators': [237180, 331128, 23544], 'label': '472392.rw.72.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '72.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BN', 'subgroup_fusion': None, 'weyl_group': None}
id: 217181357
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 4, 'diagramx': [28, -1, 1684, -1], 'generators': [79808, 331128, 23544], 'label': '472392.rw.72.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '72.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BO', 'subgroup_fusion': None, 'weyl_group': '1458.1573'}
id: 217181358
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 8, 'diagramx': [1086, -1, 2041, -1], 'generators': [466436, 246252, 23544], 'label': '472392.rw.72.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '72.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BP', 'subgroup_fusion': None, 'weyl_group': '729.453'}
id: 217181359
{'ambient': '472392.rw', 'aut_centralizer_order': None, 'aut_label': '72.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.A', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': None, 'contains': None, 'core': '472392.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [232, -1, 1753, -1], 'generators': [113276, 401916, 39312, 4536], 'label': '472392.rw.72.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.I', 'old_label': '72.bq1', 'projective_image': '472392.rw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BQ', 'subgroup_fusion': None, 'weyl_group': '486.222'}

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.