LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-21T17:45:00.053140

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': '36.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [6, 6, 18, 12], 'aut_gens': [[1, 18, 324, 972, 2916, 8748], [21007, 1422, 22356, 23976, 17496, 5832], [4429, 3474, 6480, 19440, 5832, 17496], [15001, 11250, 1944, 9396, 17496, 5832], [11077, 25902, 21384, 23976, 8748, 5832]], 'aut_group': None, 'aut_hash': 5213678477189287054, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 472392, 'aut_permdeg': 216, 'aut_perms': [3916176053721125187064069145243729732932417997494715366064623933346220889072721889512117161674205692876595258462783341680287927583446054417320518397248191109836016824096858623344215199919412208665352397750703030566407653629001593751213289845501263925630215578163595625210050161589462786171157516200368781217832317933786070948826695501934390428011431715277032888142034702509342193863596807185667682094389968638267, 1873504640772140794808710633452887989977990559592957777395929040986049997174882422395834352253233052584808938470352992615211763739332502703539980973711045587647498439048856648771660703484327888527099223046054904664735826319908900265614229037183037578937984619640146391978645531162199465793201472681963058032430869798101999640732716422531923144627695018464440828461312848829326778303540262465922263837082892796532, 7393527043336311694552391727888267340221011713835292784560755380647326325462432314614031395041624568842952305504216671349660374504480908773417666939592453424942393855083826829275955662410868973821631901298928838752999181378439126168810882422571376957325507473715890597294903911034246543860230503987676356703637404109078370473808831971304580502828421033040922478905205664628383861563958484683188485762545974209580, 8757880857466692522495520189774079764914886918966305164541346280805419748425227983349397582653414271750208780854137704771327666074131111605783390818342730510910325501906795146030894327101568371113281004144058011234138435308962431550634694312506801324692202691816149324006703165340014908075838049354594566152615509120617514465211627378624458168784798629816407155831797224342213584117918397834581198901600833531984], 'aut_phi_ratio': 54.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [2, 81, 2, 1], [3, 1, 1, 2], [3, 2, 1, 3], [3, 2, 2, 3], [3, 4, 1, 9], [3, 4, 2, 3], [3, 12, 3, 9], [3, 18, 2, 3], [3, 36, 2, 3], [6, 81, 1, 2], [6, 81, 2, 2], [6, 162, 1, 3], [6, 162, 2, 3], [6, 486, 2, 3], [9, 18, 3, 2], [9, 27, 3, 2], [9, 36, 3, 2], [9, 36, 9, 4], [9, 36, 18, 2], [9, 54, 1, 3], [9, 54, 6, 2], [9, 108, 1, 6], [9, 108, 2, 3], [9, 108, 3, 2], [18, 243, 3, 2], [18, 243, 6, 2], [18, 486, 1, 3], [18, 486, 3, 2], [18, 486, 6, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^5.C_3^2.C_6.C_6^2', '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': 454905503853125927, 'autcentquo_nilpotent': False, 'autcentquo_order': 157464, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^5.C_3.C_6.C_6^2', 'cc_stats': [[1, 1, 1], [2, 81, 3], [3, 1, 2], [3, 2, 9], [3, 4, 15], [3, 12, 27], [3, 18, 6], [3, 36, 6], [6, 81, 6], [6, 162, 9], [6, 486, 6], [9, 18, 6], [9, 27, 6], [9, 36, 78], [9, 54, 15], [9, 108, 18], [18, 243, 18], [18, 486, 21]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '729.107', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 271, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 81, 1, 3], [3, 1, 2, 1], [3, 2, 1, 3], [3, 2, 2, 3], [3, 4, 1, 3], [3, 4, 2, 6], [3, 12, 1, 3], [3, 12, 2, 12], [3, 18, 1, 2], [3, 18, 2, 2], [3, 36, 1, 2], [3, 36, 2, 2], [6, 81, 2, 3], [6, 162, 1, 3], [6, 162, 2, 3], [6, 486, 1, 2], [6, 486, 2, 2], [9, 18, 6, 1], [9, 27, 6, 1], [9, 36, 6, 13], [9, 54, 1, 1], [9, 54, 2, 1], [9, 54, 6, 2], [9, 108, 1, 2], [9, 108, 2, 5], [9, 108, 6, 1], [18, 243, 6, 3], [18, 486, 1, 1], [18, 486, 2, 1], [18, 486, 6, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 18, 'exponents_of_order': [8, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 36]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '324.167', 'hash': 7147256652985429604, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 18, 3, 3, 3, 3], 'inner_gens': [[1, 17262, 23652, 10692, 2916, 17496], [10297, 18, 18144, 7776, 5832, 17496], [11665, 9414, 324, 972, 2916, 8748], [19441, 4878, 324, 972, 2916, 8748], [1, 5850, 324, 972, 2916, 8748], [17497, 17514, 324, 972, 2916, 8748]], 'inner_hash': 8553087287890717429, 'inner_nilpotent': False, 'inner_order': 8748, 'inner_split': None, 'inner_tex': 'C_3^4.C_3^3.C_2^2', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 36], [2, 54], [4, 45], [6, 6], [12, 93], [18, 12], [36, 6]], 'label': '26244.kk', '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': True, 'name': 'C3^5.(S3*C18)', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 90, 'number_characteristic_subgroups': 31, 'number_conjugacy_classes': 252, 'number_divisions': 91, 'number_normal_subgroups': 67, 'number_subgroup_autclasses': 1777, 'number_subgroup_classes': 5095, 'number_subgroups': 159745, 'old_label': None, 'order': 26244, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 243], [3, 728], [6, 4860], [9, 5832], [18, 14580]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [3, 6, 3], 'outer_gen_pows': [21222, 108, 22167], 'outer_gens': [[18901, 450, 3564, 10692, 5832, 17496], [16837, 1422, 9720, 20736, 8748, 2916], [7381, 18990, 648, 21384, 5832, 8748]], 'outer_group': '54.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 54, 'outer_permdeg': 18, 'outer_perms': [2720990582986320, 3113404510940773, 4728249201559662], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3\\times C_3^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 9], [6, 6], [8, 6], [12, 13], [18, 4], [24, 22], [36, 6], [72, 11]], 'representations': {'PC': {'code': '101308769791437650471142740218155861412443887021180352791749675813489025736825830036312534621046892948927', 'gens': [1, 4, 7, 8, 9, 10], 'pres': [10, -2, -3, -3, -2, -3, -3, -3, -3, -3, -3, 20, 71, 690483, 417253, 113, 1175404, 443714, 194, 12965, 1655646, 113416, 70596, 34696, 855367, 388817, 34597, 15167, 29198, 1749609, 97239]}, 'Perm': {'d': 36, 'gens': [361660178585735233773798715303872216113853, 63831059419055940332320101136486003906108]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 18], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^5.(S_3\\times C_{18})', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}

Column	Type
aut_label	text
centralizer	text
counter	integer
group_counter	integer
group_order	numeric
label	text
order	integer
powers	integer[]
representative	numeric
size	numeric

gps_conj_classes • Show schema
Showing the first 100 of 252 matching records in this table.

id: 156923299
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 271, 'group_order': 26244, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 156923410
{'aut_label': '2A', 'centralizer': '81.b1', 'counter': 2, 'group_counter': 271, 'group_order': 26244, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 9, 'size': 81}
id: 156923474
{'aut_label': '2A', 'centralizer': '81.b1', 'counter': 3, 'group_counter': 271, 'group_order': 26244, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 18495, 'size': 81}
id: 156923485
{'aut_label': '2C', 'centralizer': '81.f1', 'counter': 4, 'group_counter': 271, 'group_order': 26244, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 13770, 'size': 81}
id: 156923496
{'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 271, 'group_order': 26244, 'label': '3A1', 'order': 3, 'powers': [6, 1], 'representative': 6, 'size': 1}
id: 156923507
{'aut_label': '3A-1', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 271, 'group_order': 26244, 'label': '3A-1', 'order': 3, 'powers': [5, 1], 'representative': 12, 'size': 1}
id: 156923518
{'aut_label': '3B', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 271, 'group_order': 26244, 'label': '3B', 'order': 3, 'powers': [7, 1], 'representative': 5832, 'size': 2}
id: 156923529
{'aut_label': '3B', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 271, 'group_order': 26244, 'label': '3C', 'order': 3, 'powers': [8, 1], 'representative': 17496, 'size': 2}
id: 156923540
{'aut_label': '3D', 'centralizer': '2.b1', 'counter': 9, 'group_counter': 271, 'group_order': 26244, 'label': '3D', 'order': 3, 'powers': [9, 1], 'representative': 108, 'size': 2}
id: 156923300
{'aut_label': '3E1', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 271, 'group_order': 26244, 'label': '3E1', 'order': 3, 'powers': [11, 1], 'representative': 5838, 'size': 2}
id: 156923311
{'aut_label': '3E-1', 'centralizer': '2.a1', 'counter': 11, 'group_counter': 271, 'group_order': 26244, 'label': '3E-1', 'order': 3, 'powers': [10, 1], 'representative': 2928, 'size': 2}
id: 156923322
{'aut_label': '3E1', 'centralizer': '2.a1', 'counter': 12, 'group_counter': 271, 'group_order': 26244, 'label': '3F1', 'order': 3, 'powers': [13, 1], 'representative': 17502, 'size': 2}
id: 156923333
{'aut_label': '3E-1', 'centralizer': '2.a1', 'counter': 13, 'group_counter': 271, 'group_order': 26244, 'label': '3F-1', 'order': 3, 'powers': [12, 1], 'representative': 8760, 'size': 2}
id: 156923344
{'aut_label': '3G1', 'centralizer': '2.b1', 'counter': 14, 'group_counter': 271, 'group_order': 26244, 'label': '3G1', 'order': 3, 'powers': [15, 1], 'representative': 114, 'size': 2}
id: 156923355
{'aut_label': '3G-1', 'centralizer': '2.b1', 'counter': 15, 'group_counter': 271, 'group_order': 26244, 'label': '3G-1', 'order': 3, 'powers': [14, 1], 'representative': 228, 'size': 2}
id: 156923366
{'aut_label': '3H', 'centralizer': '4.a1', 'counter': 16, 'group_counter': 271, 'group_order': 26244, 'label': '3H', 'order': 3, 'powers': [16, 1], 'representative': 11664, 'size': 4}
id: 156923377
{'aut_label': '3I', 'centralizer': '4.a1', 'counter': 17, 'group_counter': 271, 'group_order': 26244, 'label': '3I', 'order': 3, 'powers': [17, 1], 'representative': 8856, 'size': 4}
id: 156923388
{'aut_label': '3I', 'centralizer': '4.a1', 'counter': 18, 'group_counter': 271, 'group_order': 26244, 'label': '3J', 'order': 3, 'powers': [18, 1], 'representative': 3024, 'size': 4}
id: 156923399
{'aut_label': '3K1', 'centralizer': '4.a1', 'counter': 19, 'group_counter': 271, 'group_order': 26244, 'label': '3K1', 'order': 3, 'powers': [20, 1], 'representative': 11772, 'size': 4}
id: 156923411
{'aut_label': '3K-1', 'centralizer': '4.a1', 'counter': 20, 'group_counter': 271, 'group_order': 26244, 'label': '3K-1', 'order': 3, 'powers': [19, 1], 'representative': 20520, 'size': 4}
id: 156923422
{'aut_label': '3L1', 'centralizer': '4.a1', 'counter': 21, 'group_counter': 271, 'group_order': 26244, 'label': '3L1', 'order': 3, 'powers': [22, 1], 'representative': 11670, 'size': 4}
id: 156923433
{'aut_label': '3L-1', 'centralizer': '4.a1', 'counter': 22, 'group_counter': 271, 'group_order': 26244, 'label': '3L-1', 'order': 3, 'powers': [21, 1], 'representative': 11676, 'size': 4}
id: 156923444
{'aut_label': '3M1', 'centralizer': '4.a1', 'counter': 23, 'group_counter': 271, 'group_order': 26244, 'label': '3M1', 'order': 3, 'powers': [24, 1], 'representative': 8862, 'size': 4}
id: 156923455
{'aut_label': '3M-1', 'centralizer': '4.a1', 'counter': 24, 'group_counter': 271, 'group_order': 26244, 'label': '3M-1', 'order': 3, 'powers': [23, 1], 'representative': 8868, 'size': 4}
id: 156923466
{'aut_label': '3M1', 'centralizer': '4.a1', 'counter': 25, 'group_counter': 271, 'group_order': 26244, 'label': '3N1', 'order': 3, 'powers': [26, 1], 'representative': 3030, 'size': 4}
id: 156923470
{'aut_label': '3M-1', 'centralizer': '4.a1', 'counter': 26, 'group_counter': 271, 'group_order': 26244, 'label': '3N-1', 'order': 3, 'powers': [25, 1], 'representative': 3036, 'size': 4}
id: 156923471
{'aut_label': '3O1', 'centralizer': '4.a1', 'counter': 27, 'group_counter': 271, 'group_order': 26244, 'label': '3O1', 'order': 3, 'powers': [28, 1], 'representative': 11778, 'size': 4}
id: 156923472
{'aut_label': '3O-1', 'centralizer': '4.a1', 'counter': 28, 'group_counter': 271, 'group_order': 26244, 'label': '3O-1', 'order': 3, 'powers': [27, 1], 'representative': 20532, 'size': 4}
id: 156923473
{'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 29, 'group_counter': 271, 'group_order': 26244, 'label': '3P1', 'order': 3, 'powers': [30, 1], 'representative': 20526, 'size': 4}
id: 156923475
{'aut_label': '3P-1', 'centralizer': '4.a1', 'counter': 30, 'group_counter': 271, 'group_order': 26244, 'label': '3P-1', 'order': 3, 'powers': [29, 1], 'representative': 11784, 'size': 4}
id: 156923476
{'aut_label': '3Q', 'centralizer': '12.i1', 'counter': 31, 'group_counter': 271, 'group_order': 26244, 'label': '3Q', 'order': 3, 'powers': [31, 1], 'representative': 1296, 'size': 12}
id: 156923477
{'aut_label': '3Q', 'centralizer': '12.i1', 'counter': 32, 'group_counter': 271, 'group_order': 26244, 'label': '3R', 'order': 3, 'powers': [32, 1], 'representative': 2268, 'size': 12}
id: 156923478
{'aut_label': '3Q', 'centralizer': '12.i1', 'counter': 33, 'group_counter': 271, 'group_order': 26244, 'label': '3S', 'order': 3, 'powers': [33, 1], 'representative': 10044, 'size': 12}
id: 156923479
{'aut_label': '3T1', 'centralizer': '12.i1', 'counter': 34, 'group_counter': 271, 'group_order': 26244, 'label': '3T1', 'order': 3, 'powers': [35, 1], 'representative': 1404, 'size': 12}
id: 156923480
{'aut_label': '3T-1', 'centralizer': '12.i1', 'counter': 35, 'group_counter': 271, 'group_order': 26244, 'label': '3T-1', 'order': 3, 'powers': [34, 1], 'representative': 1512, 'size': 12}
id: 156923481
{'aut_label': '3U1', 'centralizer': '12.i1', 'counter': 36, 'group_counter': 271, 'group_order': 26244, 'label': '3U1', 'order': 3, 'powers': [37, 1], 'representative': 1302, 'size': 12}
id: 156923482
{'aut_label': '3U-1', 'centralizer': '12.i1', 'counter': 37, 'group_counter': 271, 'group_order': 26244, 'label': '3U-1', 'order': 3, 'powers': [36, 1], 'representative': 1308, 'size': 12}
id: 156923483
{'aut_label': '3T-1', 'centralizer': '12.i1', 'counter': 38, 'group_counter': 271, 'group_order': 26244, 'label': '3V1', 'order': 3, 'powers': [39, 1], 'representative': 2376, 'size': 12}
id: 156923484
{'aut_label': '3T1', 'centralizer': '12.i1', 'counter': 39, 'group_counter': 271, 'group_order': 26244, 'label': '3V-1', 'order': 3, 'powers': [38, 1], 'representative': 2484, 'size': 12}
id: 156923486
{'aut_label': '3U1', 'centralizer': '12.i1', 'counter': 40, 'group_counter': 271, 'group_order': 26244, 'label': '3W1', 'order': 3, 'powers': [41, 1], 'representative': 2274, 'size': 12}
id: 156923487
{'aut_label': '3U-1', 'centralizer': '12.i1', 'counter': 41, 'group_counter': 271, 'group_order': 26244, 'label': '3W-1', 'order': 3, 'powers': [40, 1], 'representative': 2280, 'size': 12}
id: 156923488
{'aut_label': '3T1', 'centralizer': '12.i1', 'counter': 42, 'group_counter': 271, 'group_order': 26244, 'label': '3X1', 'order': 3, 'powers': [43, 1], 'representative': 10152, 'size': 12}
id: 156923489
{'aut_label': '3T-1', 'centralizer': '12.i1', 'counter': 43, 'group_counter': 271, 'group_order': 26244, 'label': '3X-1', 'order': 3, 'powers': [42, 1], 'representative': 11124, 'size': 12}
id: 156923490
{'aut_label': '3U1', 'centralizer': '12.i1', 'counter': 44, 'group_counter': 271, 'group_order': 26244, 'label': '3Y1', 'order': 3, 'powers': [45, 1], 'representative': 10050, 'size': 12}
id: 156923491
{'aut_label': '3U-1', 'centralizer': '12.i1', 'counter': 45, 'group_counter': 271, 'group_order': 26244, 'label': '3Y-1', 'order': 3, 'powers': [44, 1], 'representative': 10056, 'size': 12}
id: 156923492
{'aut_label': '3Z1', 'centralizer': '12.i1', 'counter': 46, 'group_counter': 271, 'group_order': 26244, 'label': '3Z1', 'order': 3, 'powers': [47, 1], 'representative': 1410, 'size': 12}
id: 156923493
{'aut_label': '3Z-1', 'centralizer': '12.i1', 'counter': 47, 'group_counter': 271, 'group_order': 26244, 'label': '3Z-1', 'order': 3, 'powers': [46, 1], 'representative': 1524, 'size': 12}
id: 156923494
{'aut_label': '3AA1', 'centralizer': '12.i1', 'counter': 48, 'group_counter': 271, 'group_order': 26244, 'label': '3AA1', 'order': 3, 'powers': [49, 1], 'representative': 2382, 'size': 12}
id: 156923495
{'aut_label': '3AA-1', 'centralizer': '12.i1', 'counter': 49, 'group_counter': 271, 'group_order': 26244, 'label': '3AA-1', 'order': 3, 'powers': [48, 1], 'representative': 2496, 'size': 12}
id: 156923497
{'aut_label': '3AA1', 'centralizer': '12.i1', 'counter': 50, 'group_counter': 271, 'group_order': 26244, 'label': '3AB1', 'order': 3, 'powers': [51, 1], 'representative': 1518, 'size': 12}
id: 156923498
{'aut_label': '3AA-1', 'centralizer': '12.i1', 'counter': 51, 'group_counter': 271, 'group_order': 26244, 'label': '3AB-1', 'order': 3, 'powers': [50, 1], 'representative': 1416, 'size': 12}
id: 156923499
{'aut_label': '3Z1', 'centralizer': '12.i1', 'counter': 52, 'group_counter': 271, 'group_order': 26244, 'label': '3AC1', 'order': 3, 'powers': [53, 1], 'representative': 2490, 'size': 12}
id: 156923500
{'aut_label': '3Z-1', 'centralizer': '12.i1', 'counter': 53, 'group_counter': 271, 'group_order': 26244, 'label': '3AC-1', 'order': 3, 'powers': [52, 1], 'representative': 2388, 'size': 12}
id: 156923501
{'aut_label': '3Z1', 'centralizer': '12.i1', 'counter': 54, 'group_counter': 271, 'group_order': 26244, 'label': '3AD1', 'order': 3, 'powers': [55, 1], 'representative': 10158, 'size': 12}
id: 156923502
{'aut_label': '3Z-1', 'centralizer': '12.i1', 'counter': 55, 'group_counter': 271, 'group_order': 26244, 'label': '3AD-1', 'order': 3, 'powers': [54, 1], 'representative': 11136, 'size': 12}
id: 156923503
{'aut_label': '3AA1', 'centralizer': '12.i1', 'counter': 56, 'group_counter': 271, 'group_order': 26244, 'label': '3AE1', 'order': 3, 'powers': [57, 1], 'representative': 11130, 'size': 12}
id: 156923504
{'aut_label': '3AA-1', 'centralizer': '12.i1', 'counter': 57, 'group_counter': 271, 'group_order': 26244, 'label': '3AE-1', 'order': 3, 'powers': [56, 1], 'representative': 10164, 'size': 12}
id: 156923505
{'aut_label': '3AF', 'centralizer': '18.h1', 'counter': 58, 'group_counter': 271, 'group_order': 26244, 'label': '3AF', 'order': 3, 'powers': [58, 1], 'representative': 18468, 'size': 18}
id: 156923506
{'aut_label': '3AF', 'centralizer': '18.h1', 'counter': 59, 'group_counter': 271, 'group_order': 26244, 'label': '3AG', 'order': 3, 'powers': [59, 1], 'representative': 3564, 'size': 18}
id: 156923508
{'aut_label': '3AH1', 'centralizer': '18.h1', 'counter': 60, 'group_counter': 271, 'group_order': 26244, 'label': '3AH1', 'order': 3, 'powers': [61, 1], 'representative': 9726, 'size': 18}
id: 156923509
{'aut_label': '3AH-1', 'centralizer': '18.h1', 'counter': 61, 'group_counter': 271, 'group_order': 26244, 'label': '3AH-1', 'order': 3, 'powers': [60, 1], 'representative': 19452, 'size': 18}
id: 156923510
{'aut_label': '3AH-1', 'centralizer': '18.h1', 'counter': 62, 'group_counter': 271, 'group_order': 26244, 'label': '3AI1', 'order': 3, 'powers': [63, 1], 'representative': 14916, 'size': 18}
id: 156923511
{'aut_label': '3AH1', 'centralizer': '18.h1', 'counter': 63, 'group_counter': 271, 'group_order': 26244, 'label': '3AI-1', 'order': 3, 'powers': [62, 1], 'representative': 21066, 'size': 18}
id: 156923512
{'aut_label': '3AJ', 'centralizer': '36.a1', 'counter': 64, 'group_counter': 271, 'group_order': 26244, 'label': '3AJ', 'order': 3, 'powers': [64, 1], 'representative': 1080, 'size': 36}
id: 156923513
{'aut_label': '3AJ', 'centralizer': '36.a1', 'counter': 65, 'group_counter': 271, 'group_order': 26244, 'label': '3AK', 'order': 3, 'powers': [65, 1], 'representative': 432, 'size': 36}
id: 156923514
{'aut_label': '3AL1', 'centralizer': '36.a1', 'counter': 66, 'group_counter': 271, 'group_order': 26244, 'label': '3AL1', 'order': 3, 'powers': [67, 1], 'representative': 1086, 'size': 36}
id: 156923515
{'aut_label': '3AL-1', 'centralizer': '36.a1', 'counter': 67, 'group_counter': 271, 'group_order': 26244, 'label': '3AL-1', 'order': 3, 'powers': [66, 1], 'representative': 1092, 'size': 36}
id: 156923516
{'aut_label': '3AL1', 'centralizer': '36.a1', 'counter': 68, 'group_counter': 271, 'group_order': 26244, 'label': '3AM1', 'order': 3, 'powers': [69, 1], 'representative': 438, 'size': 36}
id: 156923517
{'aut_label': '3AL-1', 'centralizer': '36.a1', 'counter': 69, 'group_counter': 271, 'group_order': 26244, 'label': '3AM-1', 'order': 3, 'powers': [68, 1], 'representative': 444, 'size': 36}
id: 156923519
{'aut_label': '6A1', 'centralizer': '81.b1', 'counter': 70, 'group_counter': 271, 'group_order': 26244, 'label': '6A1', 'order': 6, 'powers': [6, 2], 'representative': 14847, 'size': 81}
id: 156923520
{'aut_label': '6A-1', 'centralizer': '81.b1', 'counter': 71, 'group_counter': 271, 'group_order': 26244, 'label': '6A-1', 'order': 6, 'powers': [5, 2], 'representative': 14835, 'size': 81}
id: 156923521
{'aut_label': '6A-1', 'centralizer': '81.b1', 'counter': 72, 'group_counter': 271, 'group_order': 26244, 'label': '6B1', 'order': 6, 'powers': [5, 3], 'representative': 1821, 'size': 81}
id: 156923522
{'aut_label': '6A1', 'centralizer': '81.b1', 'counter': 73, 'group_counter': 271, 'group_order': 26244, 'label': '6B-1', 'order': 6, 'powers': [6, 3], 'representative': 1833, 'size': 81}
id: 156923523
{'aut_label': '6C1', 'centralizer': '81.f1', 'counter': 74, 'group_counter': 271, 'group_order': 26244, 'label': '6C1', 'order': 6, 'powers': [5, 4], 'representative': 4710, 'size': 81}
id: 156923524
{'aut_label': '6C-1', 'centralizer': '81.f1', 'counter': 75, 'group_counter': 271, 'group_order': 26244, 'label': '6C-1', 'order': 6, 'powers': [6, 4], 'representative': 4704, 'size': 81}
id: 156923525
{'aut_label': '6D', 'centralizer': '162.b1', 'counter': 76, 'group_counter': 271, 'group_order': 26244, 'label': '6D', 'order': 6, 'powers': [7, 2], 'representative': 2925, 'size': 162}
id: 156923526
{'aut_label': '6D', 'centralizer': '162.b1', 'counter': 77, 'group_counter': 271, 'group_order': 26244, 'label': '6E', 'order': 6, 'powers': [8, 3], 'representative': 999, 'size': 162}
id: 156923527
{'aut_label': '6F', 'centralizer': '162.cq1', 'counter': 78, 'group_counter': 271, 'group_order': 26244, 'label': '6F', 'order': 6, 'powers': [9, 4], 'representative': 5562, 'size': 162}
id: 156923528
{'aut_label': '6G1', 'centralizer': '162.b1', 'counter': 79, 'group_counter': 271, 'group_order': 26244, 'label': '6G1', 'order': 6, 'powers': [10, 2], 'representative': 2919, 'size': 162}
id: 156923530
{'aut_label': '6G-1', 'centralizer': '162.b1', 'counter': 80, 'group_counter': 271, 'group_order': 26244, 'label': '6G-1', 'order': 6, 'powers': [11, 2], 'representative': 2931, 'size': 162}
id: 156923531
{'aut_label': '6G1', 'centralizer': '162.b1', 'counter': 81, 'group_counter': 271, 'group_order': 26244, 'label': '6H1', 'order': 6, 'powers': [12, 3], 'representative': 993, 'size': 162}
id: 156923532
{'aut_label': '6G-1', 'centralizer': '162.b1', 'counter': 82, 'group_counter': 271, 'group_order': 26244, 'label': '6H-1', 'order': 6, 'powers': [13, 3], 'representative': 1005, 'size': 162}
id: 156923533
{'aut_label': '6I1', 'centralizer': '162.cq1', 'counter': 83, 'group_counter': 271, 'group_order': 26244, 'label': '6I1', 'order': 6, 'powers': [15, 4], 'representative': 13668, 'size': 162}
id: 156923534
{'aut_label': '6I-1', 'centralizer': '162.cq1', 'counter': 84, 'group_counter': 271, 'group_order': 26244, 'label': '6I-1', 'order': 6, 'powers': [14, 4], 'representative': 13890, 'size': 162}
id: 156923535
{'aut_label': '6J', 'centralizer': '486.a1', 'counter': 85, 'group_counter': 271, 'group_order': 26244, 'label': '6J', 'order': 6, 'powers': [58, 3], 'representative': 24039, 'size': 486}
id: 156923536
{'aut_label': '6J', 'centralizer': '486.a1', 'counter': 86, 'group_counter': 271, 'group_order': 26244, 'label': '6K', 'order': 6, 'powers': [59, 2], 'representative': 18009, 'size': 486}
id: 156923537
{'aut_label': '6L1', 'centralizer': '486.a1', 'counter': 87, 'group_counter': 271, 'group_order': 26244, 'label': '6L1', 'order': 6, 'powers': [60, 3], 'representative': 23925, 'size': 486}
id: 156923538
{'aut_label': '6L-1', 'centralizer': '486.a1', 'counter': 88, 'group_counter': 271, 'group_order': 26244, 'label': '6L-1', 'order': 6, 'powers': [61, 3], 'representative': 17133, 'size': 486}
id: 156923539
{'aut_label': '6L-1', 'centralizer': '486.a1', 'counter': 89, 'group_counter': 271, 'group_order': 26244, 'label': '6M1', 'order': 6, 'powers': [62, 2], 'representative': 12327, 'size': 486}
id: 156923541
{'aut_label': '6L1', 'centralizer': '486.a1', 'counter': 90, 'group_counter': 271, 'group_order': 26244, 'label': '6M-1', 'order': 6, 'powers': [63, 2], 'representative': 6159, 'size': 486}
id: 156923542
{'aut_label': '9A1', 'centralizer': '18.v1', 'counter': 91, 'group_counter': 271, 'group_order': 26244, 'label': '9A1', 'order': 9, 'powers': [93, 15], 'representative': 21214, 'size': 18}
id: 156923543
{'aut_label': '9A-1', 'centralizer': '18.v1', 'counter': 92, 'group_counter': 271, 'group_order': 26244, 'label': '9A-1', 'order': 9, 'powers': [94, 14], 'representative': 620, 'size': 18}
id: 156923544
{'aut_label': '9A-1', 'centralizer': '18.v1', 'counter': 93, 'group_counter': 271, 'group_order': 26244, 'label': '9A2', 'order': 9, 'powers': [95, 14], 'representative': 398, 'size': 18}
id: 156923545
{'aut_label': '9A1', 'centralizer': '18.v1', 'counter': 94, 'group_counter': 271, 'group_order': 26244, 'label': '9A-2', 'order': 9, 'powers': [96, 15], 'representative': 21112, 'size': 18}
id: 156923546
{'aut_label': '9A1', 'centralizer': '18.v1', 'counter': 95, 'group_counter': 271, 'group_order': 26244, 'label': '9A4', 'order': 9, 'powers': [92, 15], 'representative': 21316, 'size': 18}
id: 156923547
{'aut_label': '9A-1', 'centralizer': '18.v1', 'counter': 96, 'group_counter': 271, 'group_order': 26244, 'label': '9A-4', 'order': 9, 'powers': [91, 14], 'representative': 518, 'size': 18}
id: 156923548
{'aut_label': '9B1', 'centralizer': '27.b1', 'counter': 97, 'group_counter': 271, 'group_order': 26244, 'label': '9B1', 'order': 9, 'powers': [99, 6], 'representative': 21076, 'size': 27}
id: 156923549
{'aut_label': '9B-1', 'centralizer': '27.b1', 'counter': 98, 'group_counter': 271, 'group_order': 26244, 'label': '9B-1', 'order': 9, 'powers': [100, 5], 'representative': 9074, 'size': 27}
id: 156923550
{'aut_label': '9B-1', 'centralizer': '27.b1', 'counter': 99, 'group_counter': 271, 'group_order': 26244, 'label': '9B2', 'order': 9, 'powers': [101, 5], 'representative': 9086, 'size': 27}
id: 156923301
{'aut_label': '9B1', 'centralizer': '27.b1', 'counter': 100, 'group_counter': 271, 'group_order': 26244, 'label': '9B-2', 'order': 9, 'powers': [102, 6], 'representative': 21064, 'size': 27}

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

gps_qchar • Show schema

id: 15339965
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.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], 'schur_index': 1}
id: 15339976
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.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], 'schur_index': 1}
id: 15339987
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.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], 'schur_index': 1}
id: 15339998
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.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], 'schur_index': 1}
id: 15340009
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id: 15340020
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id: 15340031
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id: 15339969
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id: 15339970
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id: 15339971
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id: 15339972
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id: 15339973
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id: 15339974
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id: 15339975
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id: 15339977
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id: 15339978
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id: 15339979
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id: 15339980
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id: 15339981
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id: 15339989
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id: 15339990
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id: 15339991
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id: 15340053
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id: 15339966
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id: 15339967
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id: 15339968
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.1l', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -3, -3, 6, 6, 6, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, 6, -3, -3, 6, 6, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, 3, 3, 3, 3, 6, -6, -6, -3, -3, 3, 3, 3, 3, -6, 6, 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, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, -3, -3, -3, -3, -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, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15340004
{'cdim': 6, 'counter': 45, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.6a', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 0, 0, 6, 6, 6, 6, 6, -3, 6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, -3, -3, 6, 6, -3, -3, 6, 6, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 6, 6, 0, 0, -3, 0, 0, 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], 'schur_index': 1}
id: 15340005
{'cdim': 6, 'counter': 46, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.6b', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, 0, 0, -6, 6, 6, 6, 6, -3, 6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, -3, -3, 6, 6, -3, -3, 6, 6, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, -6, -6, 0, 0, 3, 0, 0, 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], 'schur_index': 1}
id: 15339992
{'cdim': 4, 'counter': 34, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.4d', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 8, -4, -4, 8, 8, -4, 8, -4, -4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, -4, 2, 2, 2, 2, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15339993
{'cdim': 4, 'counter': 35, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.4e', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 8, -4, 8, 8, -4, -4, 8, -4, 8, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, -4, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15339994
{'cdim': 4, 'counter': 36, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.4f', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, 2, 2, -4, -4, -4, -4, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15339995
{'cdim': 4, 'counter': 37, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.4g', 'multiplicity': 2, 'nt': [12, 71], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15339996
{'cdim': 4, 'counter': 38, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.4h', 'multiplicity': 2, 'nt': [12, 130], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, 5, 5, 5, 5, 5, 5, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, 5, 5, 5, 5, 5, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15339997
{'cdim': 4, 'counter': 39, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.4i', 'multiplicity': 2, 'nt': [12, 130], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 5, 5, 5, 5, 5, -4, -4, -4, -4, -4, -4, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, -4, -4, -4, -4, -4, -4, 5, 5, 5, 5, 5, 5, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15339982
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id: 15339983
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id: 15339984
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id: 15339985
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id: 15339986
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id: 15339988
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id: 15340006
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id: 15340007
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id: 15340008
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id: 15340010
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id: 15340011
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id: 15340012
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id: 15340013
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id: 15340043
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id: 15340044
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id: 15340045
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id: 15340046
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id: 15339999
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id: 15340000
{'cdim': 4, 'counter': 41, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.4k', 'multiplicity': 6, 'nt': [36, 516], 'qdim': 24, 'qvalues': [24, 0, 0, 0, -12, -12, 24, 24, 24, -12, -12, -12, -12, -12, -12, 24, 24, 24, 24, 24, -12, -12, -12, -12, -12, -12, -12, -12, -12, -12, -12, -12, -12, -12, -12, 6, 6, -12, -12, 6, 6, -12, -12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, -12, -12, -12, 6, 6, 24, -12, -12, -12, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 6, 6, 6, 6, 6, -3, -3, -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], 'schur_index': 1}
id: 15340001
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id: 15340002
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id: 15340003
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id: 15340014
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id: 15340015
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id: 15340016
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id: 15340017
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id: 15340018
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id: 15340019
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id: 15340021
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id: 15340022
{'cdim': 12, 'counter': 61, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12m', 'multiplicity': 2, 'nt': [36, 4212], 'qdim': 24, 'qvalues': [24, 0, 0, 0, -12, -12, 24, 24, -12, -12, -12, -12, -12, 6, 6, 24, -12, -12, -12, -12, -12, -12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 15, 15, -12, -12, -12, -12, 15, 15, 15, 15, -12, -12, -12, -12, 6, 6, 6, 6, 6, 6, -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], 'schur_index': 1}
id: 15340023
{'cdim': 12, 'counter': 62, 'faithful': True, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12n', 'multiplicity': 2, 'nt': [36, 12928], 'qdim': 24, 'qvalues': [24, 0, 0, 0, -12, -12, -12, -12, -12, 6, 6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -12, -12, 15, 15, -6, -6, 12, 3, 3, 3, 3, 3, 3, 3, 3, -6, -6, -6, -6, 3, 3, -6, -6, -6, -6, 3, 3, -6, -6, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340024
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id: 15340025
{'cdim': 12, 'counter': 64, 'faithful': True, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12p', 'multiplicity': 2, 'nt': [36, 12928], 'qdim': 24, 'qvalues': [24, 0, 0, 0, -12, -12, -12, -12, -12, 6, 6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -12, -12, 15, 15, -6, -6, 12, 3, 3, 3, 3, 3, 3, 3, 3, -6, -6, -6, -6, 3, 3, -6, -6, -6, -6, 3, 3, -6, -6, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, 6, 6, 6, -3, -3, -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], 'schur_index': 1}
id: 15340026
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id: 15340027
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id: 15340028
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id: 15340029
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id: 15340030
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id: 15340032
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id: 15340047
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id: 15340048
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id: 15340049
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id: 15340050
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id: 15340051
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id: 15340033
{'cdim': 12, 'counter': 71, 'faithful': True, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12w', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -36, -36, -36, -36, -36, 18, 18, 18, 18, 18, 18, 18, 18, 18, -9, -9, -9, -9, -9, -9, -9, -9, 45, 45, -36, -36, -18, -18, 36, 9, 9, 9, 9, 9, 9, 9, 9, -18, -18, -18, -18, -18, -18, 9, 9, 9, 9, -18, -18, 36, 36, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340034
{'cdim': 12, 'counter': 72, 'faithful': True, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12x', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -36, -36, -36, -36, -36, 18, 18, 18, 18, 18, 18, 18, 18, 18, -9, -9, -9, -9, -9, -9, -9, -9, 45, 45, -36, -36, -18, 36, -18, 9, 9, 9, 9, -18, -18, -18, -18, 9, 9, 9, 9, -18, -18, -18, -18, 9, 9, 36, 36, -18, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340035
{'cdim': 12, 'counter': 73, 'faithful': True, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12y', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -36, -36, -36, -36, -36, 18, 18, 18, 18, 18, 18, 18, 18, 18, -9, -9, -9, -9, -9, -9, -9, -9, 45, 45, -36, -36, 36, -18, -18, -18, -18, -18, -18, 9, 9, 9, 9, 9, 9, 9, 9, 36, 36, 9, 9, -18, -18, -18, -18, -18, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340036
{'cdim': 12, 'counter': 74, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12z', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -36, -36, -36, -36, 72, 18, 18, 18, 18, -36, -36, 18, -36, -36, 18, 18, -9, -9, 18, 18, 18, 18, -9, -9, -9, -9, -18, -18, 36, -18, -18, 9, 9, -18, -18, 9, 9, 36, 36, -18, -18, 9, 9, 9, 9, 9, 9, 9, 9, -18, -18, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340037
{'cdim': 12, 'counter': 75, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12aa', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -36, -36, -36, -36, 72, 18, 18, 18, 18, -36, -36, 18, -36, -36, 18, 18, -9, -9, 18, 18, 18, 18, -9, -9, -9, -9, -18, 36, -18, -18, -18, 9, 9, 36, 36, -18, -18, -18, -18, 9, 9, 9, 9, -18, -18, 9, 9, -18, -18, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340038
{'cdim': 12, 'counter': 76, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12ab', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -36, -36, -36, -36, 72, 18, 18, 18, 18, -36, -36, 18, -36, -36, 18, 18, -9, -9, 18, 18, 18, 18, -9, -9, -9, -9, 36, -18, -18, 36, 36, -18, -18, -18, -18, 9, 9, -18, -18, 9, 9, -18, -18, 9, 9, -18, -18, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340039
{'cdim': 12, 'counter': 77, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12ac', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, 72, 72, -36, -36, -36, -36, -36, -36, -36, -36, -36, 18, 18, 18, -9, -9, 18, 18, 18, 18, 18, 18, -9, -9, -9, -9, -18, -18, 36, 9, 9, -18, -18, 9, 9, -18, -18, -18, -18, 36, 36, 9, 9, 9, 9, 9, 9, 9, 9, -18, -18, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340040
{'cdim': 12, 'counter': 78, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12ad', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, 72, 72, -36, -36, -36, -36, -36, -36, -36, -36, -36, 18, 18, 18, -9, -9, 18, 18, 18, 18, 18, 18, -9, -9, -9, -9, -18, 36, -18, 9, 9, -18, -18, -18, -18, 36, 36, 9, 9, -18, -18, 9, 9, -18, -18, 9, 9, -18, -18, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340041
{'cdim': 12, 'counter': 79, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.12ae', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, 72, 72, -36, -36, -36, -36, -36, -36, -36, -36, -36, 18, 18, 18, -9, -9, 18, 18, 18, 18, 18, 18, -9, -9, -9, -9, 36, -18, -18, -18, -18, 36, 36, 9, 9, -18, -18, 9, 9, -18, -18, -18, -18, 9, 9, -18, -18, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340054
{'cdim': 36, 'counter': 90, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.36c', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -36, -36, -36, 72, -36, 18, 18, -36, -36, 18, 18, -36, -36, 18, 18, 18, 18, 18, 18, 18, -9, -9, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 15340055
{'cdim': 36, 'counter': 91, 'faithful': False, 'group': '26244.kk', 'group_order': 26244, 'image': None, 'label': '26244.kk.36d', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 72, 'qvalues': [72, 0, 0, 0, -36, -36, 72, -36, -36, -36, -36, 18, 18, 18, 18, -36, 18, -36, 18, 18, 18, 18, -9, -9, 18, 18, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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}

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

gps_char • Show schema
Showing the first 100 of 252 matching records in this table.

id: 35157160
{'center': '1.a1', 'center_index': 1, 'center_order': 26244, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '26244.kk', 'group_counter': 271, 'group_order': 26244, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 26244, 'label': '26244.kk.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 35157271
{'center': '1.a1', 'center_index': 1, 'center_order': 26244, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '26244.kk', 'group_counter': 271, 'group_order': 26244, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 13122, 'label': '26244.kk.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 35157335
{'center': '1.a1', 'center_index': 1, 'center_order': 26244, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '26244.kk', 'group_counter': 271, 'group_order': 26244, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 13122, 'label': '26244.kk.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 35157346
{'center': '1.a1', 'center_index': 1, 'center_order': 26244, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '26244.kk', 'group_counter': 271, 'group_order': 26244, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 13122, 'label': '26244.kk.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 35157357
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id: 35157368
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id: 35157379
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id: 35157390
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id: 35157401
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id: 35157161
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id: 35157172
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id: 35157183
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id: 35157194
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id: 35157205
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id: 35157216
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id: 35157227
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id: 35157238
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id: 35157249
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id: 35157260
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id: 35157272
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id: 35157283
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id: 35157294
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id: 35157305
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id: 35157316
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id: 35157327
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id: 35157331
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id: 35157333
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id: 35157334
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id: 35157336
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id: 35157337
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id: 35157338
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id: 35157339
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id: 35157343
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id: 35157344
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id: 35157345
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id: 35157347
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id: 35157348
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id: 35157349
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id: 35157350
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id: 35157351
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id: 35157352
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id: 35157353
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id: 35157354
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id: 35157355
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id: 35157356
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id: 35157358
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id: 35157359
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id: 35157360
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id: 35157361
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id: 35157362
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id: 35157363
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id: 35157364
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id: 35157365
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id: 35157366
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id: 35157367
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id: 35157369
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id: 35157370
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id: 35157371
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id: 35157372
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id: 35157373
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id: 35157374
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id: 35157375
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id: 35157376
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id: 35157377
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id: 35157378
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id: 35157380
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id: 35157381
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id: 35157382
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id: 35157383
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id: 35157384
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id: 35157385
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id: 35157386
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id: 35157387
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id: 35157388
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id: 35157389
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id: 35157391
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id: 35157392
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id: 35157393
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id: 35157394
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id: 35157395
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id: 35157396
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id: 35157397
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id: 35157398
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id: 35157399
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id: 35157400
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id: 35157402
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id: 35157403
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id: 35157404
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id: 35157405
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id: 35157406
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id: 35157407
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id: 35157408
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id: 35157409
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id: 35157410
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id: 35157411
{'center': '36.d1', 'center_index': 36, 'center_order': 729, 'counter': 99, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '26244.kk', 'group_counter': 271, 'group_order': 26244, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.c1', 'kernel_order': 243, 'label': '26244.kk.4f2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -1]], [[4, 1]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, -1]], [[4, 1]], [[4, 1]], [[4, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[4, 1]], [[4, -1]], [[4, -1]], [[4, 1]], [[4, 1]], [[4, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35157162
{'center': '108.b1', 'center_index': 108, 'center_order': 243, 'counter': 100, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '26244.kk', 'group_counter': 271, 'group_order': 26244, 'image': None, 'image_isoclass': '108.40', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 243, 'label': '26244.kk.4g1', 'nt': [12, 71], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema
Showing the first 100 of 1777 matching records in this table.

id: 181404495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 26244, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '26244.kk.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', 'R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '26244.kk', 'subgroup_hash': 7147256652985429604, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^5.(S_3\\times C_{18})', 'supersolvable': True, 'sylow': 0}
id: 181405384
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 13122, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.2.a1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7269762873389147168, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^3.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 181405495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 13122, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': ['C1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7483748125783554959, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 181405606
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 8748, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.3.a1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '8748.ip', 'subgroup_hash': 8907137095831692534, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^5:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405717
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 4374, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, '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': '8748.hw', 'subgroup_hash': 4134298612632692994, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^4:(S_3\\times C_{18})', 'supersolvable': True, 'sylow': 0}
id: 181405828
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 4374, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.3.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '8748.mc', 'subgroup_hash': 4188675173849583614, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^4.(S_3\\times C_{18})', 'supersolvable': True, 'sylow': 0}
id: 181405939
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 6561, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '26244.kk.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6561.262217', 'subgroup_hash': 8785813721628222331, 'subgroup_order': 6561, 'subgroup_tex': 'C_3^5.C_3^3', 'supersolvable': True, 'sylow': 3}
id: 181406050
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4374, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7729020623363110291, 'subgroup_order': 4374, 'subgroup_tex': 'C_3\\times (C_3^4.C_3^2):C_2', 'supersolvable': True, 'sylow': 0}
id: 181406161
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4374, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6427692407187146719, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^2.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
id: 181404496
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 4374, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1291867231387128575, 'subgroup_order': 4374, 'subgroup_tex': 'C_3\\times (C_3^5.C_3):C_2', 'supersolvable': True, 'sylow': 0}
id: 181404607
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 4374, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1291867231387128575, 'subgroup_order': 4374, 'subgroup_tex': 'C_3\\times (C_3^5.C_3):C_2', 'supersolvable': True, 'sylow': 0}
id: 181404718
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 2187, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': None, 'subgroup_hash': 2539335856569382777, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^5.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 181404829
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 2187, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': None, 'subgroup_hash': 385130689794028204, 'subgroup_order': 4374, 'subgroup_tex': '(C_3^3\\times C_9).C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 181404940
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': None, 'subgroup_hash': 385130689794028204, 'subgroup_order': 4374, 'subgroup_tex': '(C_3^3\\times C_9).C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 181405051
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1458, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': None, 'subgroup_hash': 6427692407187146719, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^2.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
id: 181405162
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': None, 'subgroup_hash': 5699160797334635130, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^5.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 181405273
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 2187, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': None, 'subgroup_hash': 1125811869595889654, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^5.C_3.C_6', 'supersolvable': True, 'sylow': 0}
id: 181405362
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1458, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': None, 'subgroup_hash': 1358413977099251878, 'subgroup_order': 4374, 'subgroup_tex': 'C_3\\times (C_3\\times C_3\\times C_3^2:C_9):C_2', 'supersolvable': True, 'sylow': 0}
id: 181405373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 2916, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ih', 'subgroup_hash': 3151363058132922209, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405385
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '2916.hq', 'subgroup_hash': 45301609447718650, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4:(C_2\\times C_{18})', 'supersolvable': True, 'sylow': 0}
id: 181405396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 729, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '2916.hl', 'subgroup_hash': 2335793295017478494, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^3:(S_3\\times C_{18})', 'supersolvable': True, 'sylow': 0}
id: 181405407
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 729, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.9.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '2916.kp', 'subgroup_hash': 8718274873742516, 'subgroup_order': 2916, 'subgroup_tex': 'C_9:(C_9\\times S_3^2)', 'supersolvable': True, 'sylow': 0}
id: 181405418
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1458, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.9.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '2916.jg', 'subgroup_hash': 3233267602313280953, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
id: 181405429
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1458, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.9.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '2916.ic', 'subgroup_hash': 7449383883967843882, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 2187, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '2187.5878', 'subgroup_hash': 8913683563257941874, 'subgroup_order': 2187, 'subgroup_tex': 'C_3\\times C_3^5.C_3', 'supersolvable': True, 'sylow': 0}
id: 181405451
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 2187, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2187.5878', 'subgroup_hash': 8913683563257941874, 'subgroup_order': 2187, 'subgroup_tex': 'C_3\\times C_3^5.C_3', 'supersolvable': True, 'sylow': 0}
id: 181405462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 2187, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '2187.399', 'subgroup_hash': 2864289712745706747, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^5.C_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405473
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '2187.5884', 'subgroup_hash': 2437257725710235401, 'subgroup_order': 2187, 'subgroup_tex': 'C_3\\times C_3^4.C_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '2187.395', 'subgroup_hash': 2653269035379357496, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^4.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 181405496
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 729, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '2187.5884', 'subgroup_hash': 2437257725710235401, 'subgroup_order': 2187, 'subgroup_tex': 'C_3\\times C_3^4.C_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405507
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '2187.395', 'subgroup_hash': 2653269035379357496, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^4.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 181405518
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '2187.395', 'subgroup_hash': 2653269035379357496, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^4.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 181405529
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 729, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '2187.9094', 'subgroup_hash': 5332038839457140510, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^3\\times C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
id: 181405540
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '2187.399', 'subgroup_hash': 2864289712745706747, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^5.C_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 729, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '2187.399', 'subgroup_hash': 2864289712745706747, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^5.C_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 729, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '2187.399', 'subgroup_hash': 2864289712745706747, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^5.C_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1458, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.18.a1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1415', 'subgroup_hash': 1415, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:D_9', 'supersolvable': True, 'sylow': 0}
id: 181405584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1458, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1458.694', 'subgroup_hash': 694, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:D_9', 'supersolvable': True, 'sylow': 0}
id: 181405595
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 1458, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1797', 'subgroup_hash': 1797, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 181405607
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 1458, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['C3', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1458.692', 'subgroup_hash': 692, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405618
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.1407', 'subgroup_hash': 1407, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405629
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.691', 'subgroup_hash': 691, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405640
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.691', 'subgroup_hash': 691, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405651
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 729, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.1798', 'subgroup_hash': 1798, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
id: 181405662
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.1411', 'subgroup_hash': 1411, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:D_9', 'supersolvable': True, 'sylow': 0}
id: 181405673
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.1411', 'subgroup_hash': 1411, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:D_9', 'supersolvable': True, 'sylow': 0}
id: 181405684
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405695
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405706
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.1420', 'subgroup_hash': 1420, 'subgroup_order': 1458, 'subgroup_tex': '(C_3^2\\times C_9):C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405718
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '1458.674', 'subgroup_hash': 674, 'subgroup_order': 1458, 'subgroup_tex': '(C_3^2\\times C_9):C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405729
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.674', 'subgroup_hash': 674, 'subgroup_order': 1458, 'subgroup_tex': '(C_3^2\\times C_9):C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405740
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1420', 'subgroup_hash': 1420, 'subgroup_order': 1458, 'subgroup_tex': '(C_3^2\\times C_9):C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405751
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.674', 'subgroup_hash': 674, 'subgroup_order': 1458, 'subgroup_tex': '(C_3^2\\times C_9):C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405762
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.694', 'subgroup_hash': 694, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:D_9', 'supersolvable': True, 'sylow': 0}
id: 181405773
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1418', 'subgroup_hash': 1418, 'subgroup_order': 1458, 'subgroup_tex': '(C_3^2\\times C_9):C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405784
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.718', 'subgroup_hash': 718, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^3.(C_3\\times C_{18})', 'supersolvable': True, 'sylow': 0}
id: 181405795
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405806
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1744', 'subgroup_hash': 1744, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405817
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405829
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405840
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405851
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405862
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405873
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.1409', 'subgroup_hash': 1409, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405884
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.692', 'subgroup_hash': 692, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405895
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '1458.692', 'subgroup_hash': 692, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405906
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 162, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.18.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.be1', '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': '1458.1410', 'subgroup_hash': 1410, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405917
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.421', 'subgroup_hash': 421, 'subgroup_order': 972, 'subgroup_tex': 'S_3\\times C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405928
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.797', 'subgroup_hash': 797, 'subgroup_order': 972, 'subgroup_tex': 'C_9\\times C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405940
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.888', 'subgroup_hash': 888, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405951
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.421', 'subgroup_hash': 421, 'subgroup_order': 972, 'subgroup_tex': 'S_3\\times C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405962
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.423', 'subgroup_hash': 423, 'subgroup_order': 972, 'subgroup_tex': 'S_3\\times C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 181405973
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.889', 'subgroup_hash': 889, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405984
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.889', 'subgroup_hash': 889, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 181405995
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.420', 'subgroup_hash': 420, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 181406006
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.796', 'subgroup_hash': 796, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 181406017
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.893', 'subgroup_hash': 893, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 181406028
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.27.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, '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': '972.450', 'subgroup_hash': 450, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 181406039
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 729, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
id: 181406051
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 729, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406062
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 729, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406073
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 729, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '729.417', 'subgroup_hash': 417, 'subgroup_order': 729, 'subgroup_tex': 'C_3^2.C_3^4', 'supersolvable': True, 'sylow': 0}
id: 181406084
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 729, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.kk.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4', 'D', 'L1', 'D1', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '729.107', 'subgroup_hash': 107, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406095
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 81, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406106
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 81, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '729.497', 'subgroup_hash': 497, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 181406117
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406128
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 81, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.497', 'subgroup_hash': 497, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 181406139
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 81, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406150
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406162
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406173
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406184
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 243, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406195
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 243, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406206
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406217
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
id: 181406228
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.103', 'subgroup_hash': 103, 'subgroup_order': 729, 'subgroup_tex': 'C_3^2.C_9^2', 'supersolvable': True, 'sylow': 0}
id: 181406239
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.417', 'subgroup_hash': 417, 'subgroup_order': 729, 'subgroup_tex': 'C_3^2.C_3^4', 'supersolvable': True, 'sylow': 0}
id: 181406250
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 81, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.103', 'subgroup_hash': 103, 'subgroup_order': 729, 'subgroup_tex': 'C_3^2.C_9^2', 'supersolvable': True, 'sylow': 0}
id: 181406261
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.103', 'subgroup_hash': 103, 'subgroup_order': 729, 'subgroup_tex': 'C_3^2.C_9^2', 'supersolvable': True, 'sylow': 0}
id: 181404497
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '26244.kk', 'ambient_counter': 271, 'ambient_order': 26244, 'ambient_tex': 'C_3^5.(S_3\\times C_{18})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.kk.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '729.103', 'subgroup_hash': 103, 'subgroup_order': 729, 'subgroup_tex': 'C_3^2.C_9^2', '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 1777 matching records in this table.

id: 181404495
{'ambient': '26244.kk', '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': '8748.a1', 'complements': ['26244.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '3.a1', '3.b1', '3.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9, 2916, 5868, 3240, 8748, 162, 6, 108, 18468, 2], 'label': '26244.kk.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '3.a1'], '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: 181404496
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.a1', '18.c1', '18.w1', '18.z1', '18.bc1'], 'core': '6.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [162, 3240, 18468, 2, 6, 8748, 2916, 108], 'label': '26244.kk.6.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.c1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.a1', '18.c1'], '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.c1', 'subgroup_fusion': None, 'weyl_group': '2916.ea'}
id: 181404497
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.g1', '12.k1'], 'contains': ['108.b1', '108.bc1', '108.bd1', '108.bg1', '108.cn1'], 'core': '108.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [3242, 19044, 8748], 'label': '26244.kk.36.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
id: 181404498
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '729.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['243.e1', '243.i1', '243.n1'], 'contains': ['1458.bd1', '1458.cn2', '2187.c1'], 'core': '26244.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [9, 8910, 11988, 9720], 'label': '26244.kk.729.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.e1', 'old_label': '729.g1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.g1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 181404499
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '729.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4374.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['243.f1', '243.i1', '243.j1', '243.o1'], 'contains': ['1458.e1', '1458.bj1', '1458.cj1', '2187.b1', '2187.c1'], 'core': '8748.b1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [9, 162, 18468, 8748], 'label': '26244.kk.729.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '729.h1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.h1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
id: 181404500
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '729.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['243.g1', '243.l1', '243.m1', '243.o1', '243.p1'], 'contains': ['1458.m1', '1458.bi1', '1458.by1', '2187.b1', '2187.d1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [10701, 162, 108, 2916], 'label': '26244.kk.729.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.c1', 'old_label': '729.i1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 181404501
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '729.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['243.h1', '243.l1', '243.n1', '243.o1'], 'contains': ['1458.v1', '1458.bl1', '1458.cc1', '2187.c1', '2187.d1'], 'core': '8748.c1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [9, 162, 108, 18468], 'label': '26244.kk.729.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.h1', 'old_label': '729.j1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 181404502
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '729.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4374.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['243.k1', '243.p1'], 'contains': ['1458.bm1', '1458.br1', '2187.d1'], 'core': '8748.c1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [10701, 162, 36, 108], 'label': '26244.kk.729.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.f1', 'old_label': '729.k1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.k1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 181404503
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['324.a1', '324.f1', '324.g1', '324.g2', '324.h1', '324.i1', '324.j1', '324.j2', '324.k1', '324.l1', '324.m1', '324.n1', '324.n2', '324.o1', '324.o2', '324.p1', '324.q1', '486.d1', '486.bk1', '486.cx1'], 'contains': ['2916.a1', '2916.b1', '2916.c1', '2916.f1', '2916.p1', '2916.bb1', '2916.bp1'], 'core': '972.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 108, 8748], 'label': '26244.kk.972.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '972.a1', 'normal_contained_in': ['324.a1'], 'normal_contains': ['2916.a1', '2916.b1', '2916.c1'], 'normalizer': '1.a1', 'old_label': '972.a1', 'projective_image': None, 'quotient_action_image': '4.2', 'quotient_action_kernel': '243.65', 'quotient_action_kernel_order': 243, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 181404504
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.b1', '324.bd1', '324.be1', '324.bf1', '324.bg1', '324.bh1', '324.bi1', '486.k1', '486.dn1'], 'contains': ['2916.a1', '2916.d1', '2916.e1', '2916.o1', '2916.by1'], 'core': '972.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 2916, 8748], 'label': '26244.kk.972.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '972.b1', 'normal_contained_in': ['324.a1', '324.b1'], 'normal_contains': ['2916.a1', '2916.d1'], 'normalizer': '1.a1', 'old_label': '972.b1', 'projective_image': None, 'quotient_action_image': '4.2', 'quotient_action_kernel': '243.63', 'quotient_action_kernel_order': 243, 'quotient_fusion': None, 'short_label': '972.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 181404505
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.c1', '324.d1', '324.el1', '324.em1', '324.en1', '324.eo1', '324.ep1', '324.eq1', '324.er1', '324.es1', '324.et1', '486.cf1', '486.dw1'], 'contains': ['2916.c1', '2916.d1', '2916.q1', '2916.bc1', '2916.co1'], 'core': '972.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [108, 2916, 8748], 'label': '26244.kk.972.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '972.c1', 'normal_contained_in': ['324.a1', '324.c1', '324.d1'], 'normal_contains': ['2916.c1', '2916.d1'], 'normalizer': '1.a1', 'old_label': '972.c1', 'projective_image': '26244.kk', 'quotient_action_image': '4.2', 'quotient_action_kernel': '243.61', 'quotient_action_kernel_order': 243, 'quotient_fusion': None, 'short_label': '972.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 181404506
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '324.c1', '324.e1', '324.ey1', '324.fl1', '324.fo1', '324.fp1', '486.bd1', '486.cg1', '486.ek1'], 'contains': ['2916.d1', '2916.x1', '2916.x2', '2916.cw1'], 'core': '972.d1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3240, 2916, 8748], 'label': '26244.kk.972.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '972.d1', 'normal_contained_in': ['324.b1', '324.c1', '324.e1'], 'normal_contains': ['2916.d1'], 'normalizer': '1.a1', 'old_label': '972.d1', 'projective_image': '26244.kk', 'quotient_action_image': '36.12', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '972.d1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
id: 181404507
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.a1', '324.r1', '324.s1', '324.s2', '324.t1', '324.u1', '324.u2', '324.u3', '324.v1', '324.v2', '486.e1'], 'contains': ['2916.a1', '2916.f1', '2916.g1', '2916.q1', '2916.r1', '2916.bq1', '2916.br1', '2916.bs1', '2916.bt1'], 'core': '2916.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 8856, 2916], 'label': '26244.kk.972.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '972.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404508
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.h1', '12.j1', '12.k1'], 'contains': ['108.bb1', '108.bc1', '108.be1', '108.bg1', '108.co1'], 'core': '324.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [21710, 19044, 8748], 'label': '26244.kk.36.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
id: 181404509
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.f1', '324.r1', '324.w1', '324.x1', '324.bd1', '486.dl1'], 'contains': ['2916.a1', '2916.h1', '2916.s1', '2916.u1', '2916.bu1'], 'core': '2916.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 21708, 8748], 'label': '26244.kk.972.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '972.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404510
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.f1', '324.r1', '324.w1', '324.y1', '324.y2', '324.be1'], 'contains': ['2916.a1', '2916.i1', '2916.t1', '2916.v1', '2916.w1', '2916.bv1', '2916.bv2'], 'core': '2916.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [21816, 6, 2916], 'label': '26244.kk.972.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404511
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '324.g1', '324.s1', '324.x1', '324.y1', '324.z1', '324.z2', '324.ba1', '324.ba2', '486.a1', '486.bl1', '486.dm1'], 'contains': ['2916.a1', '2916.j1', '2916.x1', '2916.y1', '2916.bw1'], 'core': '2916.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 18468, 8748], 'label': '26244.kk.972.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '972.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.h1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 181404512
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.h2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '324.g2', '324.s2', '324.x1', '324.y2', '486.f1', '486.g1', '486.dm2'], 'contains': ['2916.a1', '2916.j1', '2916.x2', '2916.y2', '2916.bw2'], 'core': '2916.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 18468, 2916], 'label': '26244.kk.972.h2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '972.h2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.h2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 181404513
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g1', '324.s1', '324.w1', '324.y2', '324.bb1', '324.bb2', '324.bc1', '324.bc2', '324.bc3', '324.bc4', '324.bf1', '486.bm1'], 'contains': ['2916.a1', '2916.k1', '2916.z1', '2916.ba1', '2916.bx1'], 'core': '2916.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 18576, 8748], 'label': '26244.kk.972.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '972.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.i1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 181404514
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.i2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g2', '324.s2', '324.w1', '324.y1', '324.bf1', '486.h1'], 'contains': ['2916.a1', '2916.k1', '2916.z2', '2916.ba2', '2916.bx2', '2916.bx3'], 'core': '2916.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 3348, 8748], 'label': '26244.kk.972.i2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '972.i2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.i2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404515
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.i1', '324.t1', '324.z1', '324.z2', '324.bb1', '324.bb2', '324.bg1', '486.b1', '486.i1', '486.cy1'], 'contains': ['2916.a1', '2916.l1'], 'core': '2916.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [3242, 2916], 'label': '26244.kk.972.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '972.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404516
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.n1', '324.u1', '324.u2', '324.z1', '324.z2', '324.bb1', '324.bb2', '324.bh1', '486.c1'], 'contains': ['2916.a1', '2916.m1'], 'core': '2916.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2, 2916], 'label': '26244.kk.972.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '972.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.k1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404517
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.n2', '324.u3', '324.ba1', '324.ba2', '324.bc1', '324.bc2', '324.bc3', '324.bc4', '324.bh1', '486.j1'], 'contains': ['2916.a1', '2916.m1'], 'core': '2916.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2, 8748], 'label': '26244.kk.972.k2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.l1', 'old_label': '972.k2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.k2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404518
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.q1', '324.v1', '324.v2', '324.ba1', '324.ba2', '324.bc1', '324.bc2', '324.bc3', '324.bc4', '324.bi1'], 'contains': ['2916.a1', '2916.n1'], 'core': '2916.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18470, 8748], 'label': '26244.kk.972.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.p1', 'old_label': '972.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.l1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404519
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.g1', '12.j1', '12.l1'], 'contains': ['108.bb1', '108.bc1', '108.bf1', '108.bh1', '108.cp1'], 'core': '324.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [18470, 576, 8748], 'label': '26244.kk.36.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
id: 181404520
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.bj1', '324.bj2', '324.bk1', '324.bl1', '324.bm1', '324.bn1', '324.bo1', '324.bo2', '324.bp1', '324.bp2', '324.bq1', '324.bq2', '324.br1', '324.bs1', '324.bt1', '324.bu1', '324.bv1', '324.bv2', '324.bw1', '324.bw2', '486.cz1'], 'contains': ['2916.b1', '2916.e1', '2916.g1', '2916.bc1', '2916.bd1', '2916.bz1', '2916.ca1', '2916.cb1', '2916.cc1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 108, 11664], 'label': '26244.kk.972.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '972.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404521
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.f1', '324.bj1', '324.bj2', '324.bx1', '324.by1', '324.by2', '324.bz1', '324.ca1', '324.ca2', '486.da1'], 'contains': ['2916.b1', '2916.h1', '2916.i1', '2916.be1', '2916.bf1', '2916.cd1', '2916.ce1', '2916.cf1', '2916.cg1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [108, 114, 12960], 'label': '26244.kk.972.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '972.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404522
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g1', '324.g2', '324.bk1', '324.ca1', '324.ca2', '486.l1', '486.bn1', '486.db1'], 'contains': ['2916.b1', '2916.j1', '2916.k1', '2916.bg1', '2916.bh1', '2916.ch1', '2916.ci1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6, 3240, 108], 'label': '26244.kk.972.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.e1', 'old_label': '972.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 181404523
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.h1', '324.bl1', '324.bm1', '324.bx1', '324.cb1', '324.cc1', '324.cd1', '486.cu1'], 'contains': ['2916.b1', '2916.cj1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [578, 108], 'label': '26244.kk.972.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '972.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.p1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404524
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.bx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.i1', '324.bn1', '324.cb1', '324.cd1', '324.ce1', '486.m1', '486.cv1'], 'contains': ['2916.b1', '2916.l1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [3242, 108], 'label': '26244.kk.972.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '972.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404525
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.j1', '324.j2', '324.bo1', '324.bo2', '324.by1', '324.by2'], 'contains': ['2916.b1', '2916.ck1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [19046, 108], 'label': '26244.kk.972.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1', 'old_label': '972.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404526
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.k1', '324.bp1', '324.bp2', '324.by1', '324.by2', '324.cc1', '324.cf1', '324.cf2', '324.cg1', '324.cg2'], 'contains': ['2916.b1', '2916.cl1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [15806, 108], 'label': '26244.kk.972.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '972.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.s1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404527
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.l1', '324.bq1', '324.bq2', '324.bx1', '324.bz1'], 'contains': ['2916.b1', '2916.cm1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [16778, 108], 'label': '26244.kk.972.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1', 'old_label': '972.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404528
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.h1', '324.bl1', '324.br1', '324.bz1', '324.cb1', '324.ce1', '324.cf1', '324.cf2'], 'contains': ['2916.b1', '2916.cn1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [9326, 108], 'label': '26244.kk.972.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '972.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.u1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404529
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.m1', '324.bs1', '324.cb1', '324.cd1', '324.ce1', '486.bo1', '486.cw1'], 'contains': ['2916.b1', '2916.bi1', '2916.bj1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6, 6084], 'label': '26244.kk.972.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '972.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.v1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 181404530
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.h1', '12.j1', '12.k1'], 'contains': ['108.q1', '108.bb1', '108.bd1', '108.be1', '108.bg1'], 'core': '324.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [13934, 19044, 2916], 'label': '26244.kk.36.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
id: 181404531
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.n1', '324.n2', '324.bt1', '324.cg1', '324.cg2', '486.n1'], 'contains': ['2916.b1', '2916.m1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [21710, 108], 'label': '26244.kk.972.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '972.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404532
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.o1', '324.o2', '324.bu1', '324.cg1', '324.cg2', '486.bp1'], 'contains': ['2916.b1', '2916.bk1', '2916.bm1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 576], 'label': '26244.kk.972.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '972.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.x1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 181404533
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.p1', '324.bv1', '324.bv2', '324.cc1', '324.cf1', '324.cf2'], 'contains': ['2916.b1', '2916.bl1', '2916.bn1', '2916.bo1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [19044, 6], 'label': '26244.kk.972.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.s1', 'old_label': '972.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.y1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404534
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.q1', '324.bw1', '324.bw2', '324.cc1', '324.cf1', '324.cf2'], 'contains': ['2916.b1', '2916.n1'], 'core': '2916.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18470, 108], 'label': '26244.kk.972.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.s1', 'old_label': '972.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.z1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404535
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.ch1', '324.ch2', '324.ci1', '324.cj1', '324.ck1', '324.ck2', '324.cl1', '324.cl2', '324.cl3'], 'contains': ['2916.e1', '2916.f1', '2916.g1', '2916.co1', '2916.cp1', '2916.cq1', '2916.da1', '2916.db1', '2916.dg1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 8856, 11664], 'label': '26244.kk.972.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '972.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404536
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.bd1', '324.bj1', '324.ch1', '324.cm1', '324.cn1', '324.co1', '324.cp1', '486.do1'], 'contains': ['2916.e1', '2916.h1', '2916.cr1', '2916.ct1', '2916.dl1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 12960, 11664], 'label': '26244.kk.972.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '972.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bb1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 181404537
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bd1', '324.bj2', '324.ch2', '324.cm2', '324.cp1', '486.do2'], 'contains': ['2916.e1', '2916.h1', '2916.cr2', '2916.ct2', '2916.dl2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 21708, 20412], 'label': '26244.kk.972.bb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '972.bb2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bb2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404538
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.be1', '324.bj1', '324.ch1', '324.cm2', '324.cq1', '324.cr1', '324.cs1'], 'contains': ['2916.e1', '2916.i1', '2916.cs1', '2916.cu1', '2916.cv1', '2916.dm1', '2916.dm2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [13068, 6, 11664], 'label': '26244.kk.972.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '972.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bc1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404539
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.be1', '324.bj2', '324.ch2', '324.cm1', '324.cs1'], 'contains': ['2916.e1', '2916.i1', '2916.cs2', '2916.cu2', '2916.cv2', '2916.dm3'], 'core': '8748.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [21816, 6, 20412], 'label': '26244.kk.972.bc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.bc2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bc2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404540
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.b1', '324.bk1', '324.ci1', '324.cp1', '324.cs1', '486.dp1'], 'contains': ['2916.e1', '2916.j1', '2916.cw1', '2916.cx1', '2916.dn1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 18468, 11664], 'label': '26244.kk.972.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '972.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bd1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 181404541
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.g1', '12.j1', '12.l1'], 'contains': ['108.r1', '108.bb1', '108.bd1', '108.bf1', '108.bh1'], 'core': '324.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [18470, 24552, 8748], 'label': '26244.kk.36.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
id: 181404542
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bf1', '324.bk1', '324.ci1', '324.cm1', '324.cm2', '324.cs1'], 'contains': ['2916.e1', '2916.k1', '2916.cy1', '2916.cz1', '2916.cz2', '2916.do1', '2916.do2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6, 3348, 11664], 'label': '26244.kk.972.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.be1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404543
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bg1', '324.bn1', '324.cj1', '324.cn1', '324.cq1', '486.dc1'], 'contains': ['2916.e1', '2916.l1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [3242, 11664], 'label': '26244.kk.972.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.w1', 'old_label': '972.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404544
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bh1', '324.bt1', '324.ck1', '324.ck2', '324.co1', '324.cr1'], 'contains': ['2916.e1', '2916.m1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [21710, 11664], 'label': '26244.kk.972.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '972.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bg1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404545
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bi1', '324.bw1', '324.cl1', '324.cn1', '324.cq1'], 'contains': ['2916.e1', '2916.n1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18470, 20412], 'label': '26244.kk.972.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '972.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bh1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404546
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bi1', '324.bw2', '324.cl2', '324.cl3', '324.co1', '324.cr1'], 'contains': ['2916.e1', '2916.n1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18470, 11664], 'label': '26244.kk.972.bh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '972.bh2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bh2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404547
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['324.f1', '324.r1', '324.ch1', '324.ch2', '324.ct1', '324.ct2'], 'contains': ['2916.f1', '2916.h1', '2916.i1', '2916.dc1', '2916.dd1', '2916.dd2', '2916.dp1', '2916.dq1', '2916.dr1', '2916.dr2', '2916.ds1', '2916.ds2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [3024, 21708, 3030], 'label': '26244.kk.972.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404548
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g1', '324.s2', '324.ci1', '324.ct1', '324.ct2', '486.bq1'], 'contains': ['2916.f1', '2916.j1', '2916.k1', '2916.de1', '2916.df1', '2916.dt1', '2916.du1', '2916.du2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 3240, 3024], 'label': '26244.kk.972.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '972.bj1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404549
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g2', '324.s1', '324.ci1', '324.ct1', '324.ct2', '486.o1'], 'contains': ['2916.f1', '2916.j1', '2916.k1', '2916.de2', '2916.df2', '2916.df3', '2916.dt2', '2916.du3', '2916.du4'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 3240, 8856], 'label': '26244.kk.972.bj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '972.bj2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bj2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404550
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.i1', '324.t1', '324.cj1', '486.p1'], 'contains': ['2916.f1', '2916.l1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [3242, 3024], 'label': '26244.kk.972.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '972.bk1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404551
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.n1', '324.u3', '324.ck1', '324.ck2'], 'contains': ['2916.f1', '2916.m1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2, 3024], 'label': '26244.kk.972.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.y1', 'old_label': '972.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bl1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404552
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.h1', '12.l1', '18.o1'], 'contains': ['108.c1', '108.s1', '108.bb1', '108.be1'], 'core': '108.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [21710, 6084, 8748], 'label': '26244.kk.36.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1', 'subgroup_fusion': None, 'weyl_group': '162.52'}
id: 181404553
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.n2', '324.u1', '324.ck2', '486.q1'], 'contains': ['2916.f1', '2916.m1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [21710, 3132], 'label': '26244.kk.972.bl2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '972.bl2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bl2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404554
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bl3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.n2', '324.u2', '324.ck1', '486.q2'], 'contains': ['2916.f1', '2916.m1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [21710, 3024], 'label': '26244.kk.972.bl3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1', 'old_label': '972.bl3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bl3', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404555
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.q1', '324.v1', '324.cl1', '324.cl2'], 'contains': ['2916.f1', '2916.n1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18470, 5940], 'label': '26244.kk.972.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.z1', 'old_label': '972.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bm1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404556
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.q1', '324.v2', '324.cl1', '324.cl3'], 'contains': ['2916.f1', '2916.n1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18470, 3024], 'label': '26244.kk.972.bm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bb1', 'old_label': '972.bm2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bm2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404557
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.r1', '324.bj1', '324.ch2', '324.cu1', '324.cu2'], 'contains': ['2916.g1', '2916.h1', '2916.i1', '2916.dh1', '2916.di1', '2916.di2', '2916.dv1', '2916.dy1', '2916.dy2', '2916.ec1', '2916.ed1', '2916.ed2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [11772, 12960, 23556], 'label': '26244.kk.972.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404558
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.r1', '324.bj2', '324.ch1', '324.cu1', '324.cu2'], 'contains': ['2916.g1', '2916.h1', '2916.i1', '2916.dh2', '2916.di3', '2916.dw1', '2916.dx1', '2916.eb1', '2916.ee1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [20520, 12960, 20526], 'label': '26244.kk.972.bn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.bn2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bn2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404559
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.s1', '324.s2', '324.bk1', '324.ci1', '324.cu1', '324.cu2'], 'contains': ['2916.g1', '2916.j1', '2916.k1', '2916.dj1', '2916.dk1', '2916.dk2', '2916.dz1', '2916.ea1', '2916.ea2', '2916.ef1', '2916.eg1', '2916.eg2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6, 3240, 11772], 'label': '26244.kk.972.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '972.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404560
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.t1', '324.bn1', '324.cj1'], 'contains': ['2916.g1', '2916.l1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [3242, 11772], 'label': '26244.kk.972.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.v1', 'old_label': '972.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bp1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404561
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.u1', '324.u3', '324.bt1', '324.ck1'], 'contains': ['2916.g1', '2916.m1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2, 11772], 'label': '26244.kk.972.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '972.bq1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bq1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404562
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.u2', '324.u3', '324.bt1', '324.ck2'], 'contains': ['2916.g1', '2916.m1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2, 20520], 'label': '26244.kk.972.bq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.w1', 'old_label': '972.bq2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bq2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404563
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1', '12.h1', '12.j1'], 'contains': ['108.t1', '108.bb1', '108.bg1', '108.bh1'], 'core': '324.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [10694, 11268, 2916], 'label': '26244.kk.36.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
id: 181404564
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.v1', '324.v2', '324.bw2', '324.cl1'], 'contains': ['2916.g1', '2916.n1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [18470, 23436], 'label': '26244.kk.972.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.x1', 'old_label': '972.br1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.br1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404565
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.br2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.v1', '324.bw1', '324.cl3'], 'contains': ['2916.g1', '2916.n1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18470, 14688], 'label': '26244.kk.972.br2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bc1', 'old_label': '972.br2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.br2', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404566
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.br3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.v2', '324.bw1', '324.cl2'], 'contains': ['2916.g1', '2916.n1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [18470, 20520], 'label': '26244.kk.972.br3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.t1', 'old_label': '972.br3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.br3', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 181404567
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.w1', '324.ca1', '324.cm1', '324.cm2', '324.ct1', '324.cu1', '324.cu2'], 'contains': ['2916.h1', '2916.i1', '2916.k1', '2916.eh1', '2916.ej1', '2916.ek1', '2916.em1', '2916.eq1', '2916.er1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 1080, 12960], 'label': '26244.kk.972.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '972.bs1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404568
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['324.w1', '324.ca2', '324.cm1', '324.cm2', '324.ct1', '324.ct2', '324.cu1', '324.cu2'], 'contains': ['2916.h1', '2916.i1', '2916.k1', '2916.eh2', '2916.ej2', '2916.ek2', '2916.em2', '2916.em3', '2916.eq2', '2916.eq3', '2916.er2', '2916.er3'], 'core': '8748.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 9828, 12960], 'label': '26244.kk.972.bs2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '972.bs2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bs2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404569
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.x1', '324.ca1', '324.cp1', '324.ct2', '324.cu1', '486.r1', '486.dq2'], 'contains': ['2916.h1', '2916.j1', '2916.ei1', '2916.el1', '2916.es1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6, 11988, 18468], 'label': '26244.kk.972.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.e1', 'old_label': '972.bt1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 181404570
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bt2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.x1', '324.ca2', '324.cp1', '324.ct1', '324.cu2', '486.dq1'], 'contains': ['2916.h1', '2916.j1', '2916.ei2', '2916.el2', '2916.es2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6, 3240, 9720], 'label': '26244.kk.972.bt2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '972.bt2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bt2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404571
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['324.y1', '324.y2', '324.ca1', '324.cs1', '324.ct1', '324.ct2', '324.cu2', '486.s1'], 'contains': ['2916.i1', '2916.j1', '2916.k1', '2916.en1', '2916.eo1', '2916.ep1', '2916.et1', '2916.eu1', '2916.ev1'], 'core': '8748.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6, 11988, 18576], 'label': '26244.kk.972.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '972.bu1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404572
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bu2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['324.y1', '324.y2', '324.ca2', '324.cs1', '324.ct1', '324.ct2', '324.cu1', '324.cu2'], 'contains': ['2916.i1', '2916.j1', '2916.k1', '2916.en2', '2916.en3', '2916.eo2', '2916.eo3', '2916.ep2', '2916.et2', '2916.et3', '2916.eu2', '2916.ev2'], 'core': '8748.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6, 9720, 20844], 'label': '26244.kk.972.bu2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '972.bu2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bu2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404573
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.a1', '324.cv1', '324.cw1', '324.cw2', '324.cx1', '324.cy1', '324.cy2', '324.cy3', '324.cz1', '324.cz2', '486.br1'], 'contains': ['2916.c1', '2916.o1', '2916.r1', '2916.bb1', '2916.bd1', '2916.bq1', '2916.br1', '2916.da1', '2916.db1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2922, 108, 8748], 'label': '26244.kk.972.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '972.bv1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404574
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.h1', '12.l1'], 'contains': ['108.c1', '108.bc1', '108.bd1', '108.bh1', '108.cr1'], 'core': '108.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [18470, 6084, 8748], 'label': '26244.kk.36.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
id: 181404575
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.f1', '324.cv1', '324.da1', '324.db1', '324.el1', '486.dr1'], 'contains': ['2916.c1', '2916.s1', '2916.t1', '2916.be1', '2916.dc1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [108, 21708, 8748], 'label': '26244.kk.972.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '972.bw1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 181404576
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.f1', '324.cv1', '324.da1', '324.dc1', '324.dc2', '324.em1'], 'contains': ['2916.c1', '2916.u1', '2916.v1', '2916.w1', '2916.bf1', '2916.dd1', '2916.dd2'], 'core': '2916.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [21714, 108, 8748], 'label': '26244.kk.972.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.bx1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404577
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.c1', '324.g1', '324.cw2', '324.db1', '324.dc2', '486.t1', '486.cr1', '486.ds1'], 'contains': ['2916.c1', '2916.x1', '2916.z1', '2916.bg1', '2916.de1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3240, 108, 2916], 'label': '26244.kk.972.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '972.by1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.by1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
id: 181404578
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.by2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.c1', '324.g2', '324.cw1', '324.db1', '324.dc1', '324.dd1', '324.de1', '324.df1', '324.dg1', '486.bs1', '486.bt1', '486.ds2'], 'contains': ['2916.c1', '2916.x2', '2916.z2', '2916.bg1', '2916.de2'], 'core': '2916.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [18468, 108, 2916], 'label': '26244.kk.972.by2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '972.by2', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.by2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 181404579
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g1', '324.cw2', '324.da1', '324.dc1', '324.en1', '486.u1'], 'contains': ['2916.c1', '2916.y1', '2916.ba1', '2916.bh1', '2916.df1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [3246, 108, 2916], 'label': '26244.kk.972.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1', 'old_label': '972.bz1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bz1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 181404580
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.bz2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g2', '324.cw1', '324.da1', '324.dc2', '324.dh1', '324.di1', '324.dj1', '324.dk1', '324.dl1', '324.dm1', '324.en1', '486.bu1'], 'contains': ['2916.c1', '2916.y2', '2916.ba2', '2916.bh1', '2916.df2', '2916.df3'], 'core': '2916.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [3246, 108, 8748], 'label': '26244.kk.972.bz2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '972.bz2', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bz2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 181404581
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.d1', '324.m1', '324.cx1', '324.dd1', '324.dh1', '486.bv1', '486.cs1', '486.dd1'], 'contains': ['2916.c1', '2916.bi1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6084, 8748], 'label': '26244.kk.972.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '972.ca1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ca1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
id: 181404582
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.m1', '324.cx1', '324.de1', '324.di1', '324.eo1', '486.de1'], 'contains': ['2916.c1', '2916.bj1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6090, 8748], 'label': '26244.kk.972.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '972.cb1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cb1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 181404583
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.o1', '324.cy1', '324.dd1', '324.di1', '324.ep1', '486.bw1'], 'contains': ['2916.c1', '2916.bk1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [576, 8748], 'label': '26244.kk.972.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '972.cc1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cc1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 181404584
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.cc2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.o2', '324.cy2', '324.cy3', '324.df1', '324.dj1', '324.dk1', '324.ep1', '486.ct1'], 'contains': ['2916.c1', '2916.bk1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [576, 2916], 'label': '26244.kk.972.cc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '972.cc2', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cc2', 'subgroup_fusion': None, 'weyl_group': '18.5'}
id: 181404585
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.k1', '12.l1', '18.p1'], 'contains': ['108.u1', '108.u2', '108.bc1', '108.be1', '108.bf1', '108.ct1'], 'core': '324.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2, 24552, 2916, 8748], 'label': '26244.kk.36.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', '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.bd1', 'subgroup_fusion': None, 'weyl_group': '162.52'}
id: 181404586
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.p1', '324.cz1', '324.cz2', '324.df1', '324.dl1', '324.dm1', '324.eq1'], 'contains': ['2916.c1', '2916.bl1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [19044, 8748], 'label': '26244.kk.972.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '972.cd1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cd1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 181404587
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.o1', '324.cy1', '324.de1', '324.dh1', '324.di1', '324.er1'], 'contains': ['2916.c1', '2916.bm1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [582, 8748], 'label': '26244.kk.972.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1', 'old_label': '972.ce1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ce1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 181404588
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.ce2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.o2', '324.cy2', '324.cy3', '324.dg1', '324.dl1', '324.dm1', '324.er1'], 'contains': ['2916.c1', '2916.bm1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [582, 2916], 'label': '26244.kk.972.ce2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1', 'old_label': '972.ce2', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ce2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 181404589
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.p1', '324.cz1', '324.cz2', '324.dg1', '324.dj1', '324.dl1', '324.es1'], 'contains': ['2916.c1', '2916.bn1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [19050, 8748], 'label': '26244.kk.972.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '972.cf1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cf1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 181404590
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.p1', '324.cz1', '324.cz2', '324.dg1', '324.dk1', '324.dm1', '324.et1'], 'contains': ['2916.c1', '2916.bo1'], 'core': '2916.c1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [11274, 8748], 'label': '26244.kk.972.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1', 'old_label': '972.cg1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cg1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 181404591
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.a1', '324.dn1', '324.dn2', '324.do1', '324.do2', '324.dp1', '324.dq1', '324.dq2', '324.dq3', '324.dq4', '324.dr1', '324.dr2', '324.ds1', '324.ds2'], 'contains': ['2916.o1', '2916.p1', '2916.q1', '2916.r1', '2916.bp1', '2916.bs1', '2916.bt1', '2916.cb1', '2916.cc1', '2916.da1', '2916.db1', '2916.dg1'], 'core': '8748.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [2922, 3024, 8748], 'label': '26244.kk.972.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '972.ch1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ch1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404592
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bd1', '324.cv1', '324.dn1', '324.dn2', '324.dt1', '324.dt2', '324.du1'], 'contains': ['2916.o1', '2916.s1', '2916.u1', '2916.bu1', '2916.dl1', '2916.dl2'], 'core': '8748.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [2922, 21708, 8748], 'label': '26244.kk.972.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.ci1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ci1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404593
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.be1', '324.cv1', '324.dn1', '324.dn2', '324.dt1', '324.dv1', '324.dv2'], 'contains': ['2916.o1', '2916.t1', '2916.v1', '2916.w1', '2916.bv1', '2916.dm1', '2916.dm3'], 'core': '8748.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [21816, 8754, 2916], 'label': '26244.kk.972.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.cj1', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 181404594
{'ambient': '26244.kk', 'aut_centralizer_order': None, 'aut_label': '972.cj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.be1', '324.cv1', '324.dn1', '324.dn2', '324.dt2', '324.dv1', '324.dv3'], 'contains': ['2916.o1', '2916.t1', '2916.v1', '2916.w1', '2916.bv2', '2916.dm2', '2916.dm3'], 'core': '8748.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [21816, 17502, 2916], 'label': '26244.kk.972.cj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1', 'old_label': '972.cj2', 'projective_image': '26244.kk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cj2', 'subgroup_fusion': None, 'weyl_group': '1.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.