LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-22T11:30:32.166680

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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 72, 'aut_gen_orders': [18, 12, 12, 4], 'aut_gens': [[1, 4, 36], [451, 4, 612], [391, 296, 260], [407, 508, 644], [223, 592, 196]], 'aut_group': None, 'aut_hash': 7935501427042882995, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 23328, 'aut_permdeg': 324, 'aut_perms': [16081590991859316671764281960037551388639712094954080252881782089122134475168740963818641749798934941859714944121755227733785436302391794760031015162131503681612681964026490734743977969739548693465108276639105723673813870206168107474873468578291093965983716313205930933268394125595203030498275371245057573925015567499016934499799929793021300533562205909156538644185168585820956280431675739598832701884877111687557465245197188825638515925221043747081877783693812604156239212772784938834675911749712690784963366312889236778398669938620151805661019464468698529892777830665932423445293501551375663742003779241577417329666259174306223077975281881939203245241526001706682132477413, 222168850902440016820153752470441291698438133111232355341720384998357673216923548732317685636983249296222019033921291722168731128650781813258879792913209612541142041612286498254076095781167832715597252500556296802467566006896618306610761642602424390594858393581989260388181777665097576031886034311082045075066828917686943045161632789867492103599242122826856332373947047879786440923189664771732737140673909921630370179127251462157843742760335039666940463565197233834810678911943997565418113234715663209831793121028290901350686163350776982190846077293075277170687489409610765712358693447205062389420229311265244434000733317091783697569026629176123550306948992797566966488774658, 19218318302118904508780544056870616113834586029051451976610836248606671934747294660180961349560073680632234661042029485029803677848227649141574565457165070254536094739354001566171856931380887078272748267834794326835396982880400313148917070117572897697647319089255717868924024886681226044875836437456570125665608075656975882586754263407970022932105052603919321223672528372728926943474565203915212581696088116594512890280224216066182857636736158606361688539545652806239503878975284228820299883824069725464846320981104885885176316397012365341994924499136946250598774806464832813022336774432413544276480038618458099728418761266657018763462578350199799037557312770577568600157752, 155371710701012845664043747635513138717390229465834291504879574517818036100860869095444771890777017108955011462934672607594790523545107869950740707967791437404760244384864458265707838054165954431153573570510029663152966253788776651808841941098168967527510868544296775156631721438270084651895847870697207447860241908711812375031177158037317327352871696699460565379280553393641494805770469871603354726877694852413515474802220703001330853207376160437604755217086370327642112817623597552675592019821999794371132978902884035901133014158112073811609113937343278716591781092521629217844262858394339833639842864735585969174876204801657823412343586607048266429111509891433128514594611], 'aut_phi_ratio': 108.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 81, 1, 2], [3, 4, 2, 1], [4, 81, 4, 1], [6, 4, 2, 1], [9, 4, 18, 1], [18, 4, 18, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_9^2.C_{12}.C_6.C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': '11664.lk', 'autcentquo_hash': 4509669642411733234, 'autcentquo_nilpotent': False, 'autcentquo_order': 11664, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_9^2:C_{24}:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 81, 2], [3, 4, 2], [4, 81, 4], [6, 4, 2], [9, 4, 18], [18, 4, 18]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '324.35', 'commutator_count': 1, 'commutator_label': '81.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 295, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['324.35', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 81, 1, 2], [3, 4, 1, 2], [4, 81, 2, 2], [6, 4, 1, 2], [9, 4, 3, 6], [18, 4, 3, 6]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 36, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 1, 18]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '72.45', 'hash': 295, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [4, 9, 9], 'inner_gens': [[1, 72, 340], [581, 4, 36], [381, 4, 36]], 'inner_hash': 35, 'inner_nilpotent': False, 'inner_order': 324, 'inner_split': False, 'inner_tex': 'C_9^2:C_4', 'inner_used': [1, 2], 'irrC_degree': 4, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [4, 40]], 'label': '648.295', 'linC_count': 18, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 6, 'linQ_dim': 12, 'linQ_dim_count': 6, 'linR_count': 18, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C9^2:C4', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 48, 'number_divisions': 22, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 74, 'number_subgroups': 1276, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 163], [3, 8], [4, 324], [6, 8], [9, 72], [18, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6, 6], 'outer_gen_pows': [1, 2, 1], 'outer_gens': [[1, 172, 284], [3, 76, 632], [325, 292, 64]], 'outer_group': '72.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 10, 'outer_perms': [720, 40350, 725761], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 4], [12, 12]], 'representations': {'PC': {'code': 61495217765367759772513961991141978309998402203, 'gens': [1, 3, 5], 'pres': [7, 2, 2, 3, 3, 2, 3, 3, 14, 1514, 345, 79, 6051, 346, 11904, 10721, 102, 1349, 12108, 166, 1182, 10597]}, 'Perm': {'d': 20, 'gens': [123600953843512129, 1, 2335037506744344, 265140936561700206, 393592528344800160, 399987211639843080, 32392094382437184]}}, 'schur_multiplier': [18], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_9^2:C_4', '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

id: 139761184
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 295, 'group_order': 648, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 139761195
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 295, 'group_order': 648, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 324, 'size': 1}
id: 139761206
{'aut_label': '2B', 'centralizer': '81.a1.a1', 'counter': 3, 'group_counter': 295, 'group_order': 648, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 382, 'size': 81}
id: 139761217
{'aut_label': '2C', 'centralizer': '81.a1.a1', 'counter': 4, 'group_counter': 295, 'group_order': 648, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 266, 'size': 81}
id: 139761227
{'aut_label': '3A', 'centralizer': '4.a1.a1', 'counter': 5, 'group_counter': 295, 'group_order': 648, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 216, 'size': 4}
id: 139761228
{'aut_label': '3A', 'centralizer': '4.a1.a1', 'counter': 6, 'group_counter': 295, 'group_order': 648, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 240, 'size': 4}
id: 139761229
{'aut_label': '4A1', 'centralizer': '81.a1.a1', 'counter': 7, 'group_counter': 295, 'group_order': 648, 'label': '4A1', 'order': 4, 'powers': [3, 8], 'representative': 21, 'size': 81}
id: 139761230
{'aut_label': '4A1', 'centralizer': '81.a1.a1', 'counter': 8, 'group_counter': 295, 'group_order': 648, 'label': '4A-1', 'order': 4, 'powers': [3, 7], 'representative': 363, 'size': 81}
id: 139761231
{'aut_label': '4A1', 'centralizer': '81.a1.a1', 'counter': 9, 'group_counter': 295, 'group_order': 648, 'label': '4B1', 'order': 4, 'powers': [3, 10], 'representative': 329, 'size': 81}
id: 139761185
{'aut_label': '4A1', 'centralizer': '81.a1.a1', 'counter': 10, 'group_counter': 295, 'group_order': 648, 'label': '4B-1', 'order': 4, 'powers': [3, 9], 'representative': 399, 'size': 81}
id: 139761186
{'aut_label': '6A', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 295, 'group_order': 648, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 108, 'size': 4}
id: 139761187
{'aut_label': '6A', 'centralizer': '4.a1.a1', 'counter': 12, 'group_counter': 295, 'group_order': 648, 'label': '6B', 'order': 6, 'powers': [6, 2], 'representative': 120, 'size': 4}
id: 139761188
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 13, 'group_counter': 295, 'group_order': 648, 'label': '9A1', 'order': 9, 'powers': [14, 5], 'representative': 72, 'size': 4}
id: 139761189
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 14, 'group_counter': 295, 'group_order': 648, 'label': '9A2', 'order': 9, 'powers': [15, 5], 'representative': 144, 'size': 4}
id: 139761190
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 15, 'group_counter': 295, 'group_order': 648, 'label': '9A4', 'order': 9, 'powers': [13, 5], 'representative': 288, 'size': 4}
id: 139761191
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 16, 'group_counter': 295, 'group_order': 648, 'label': '9B1', 'order': 9, 'powers': [17, 5], 'representative': 96, 'size': 4}
id: 139761192
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 17, 'group_counter': 295, 'group_order': 648, 'label': '9B2', 'order': 9, 'powers': [18, 5], 'representative': 156, 'size': 4}
id: 139761193
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 18, 'group_counter': 295, 'group_order': 648, 'label': '9B4', 'order': 9, 'powers': [16, 5], 'representative': 312, 'size': 4}
id: 139761194
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 19, 'group_counter': 295, 'group_order': 648, 'label': '9C1', 'order': 9, 'powers': [20, 6], 'representative': 80, 'size': 4}
id: 139761196
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 20, 'group_counter': 295, 'group_order': 648, 'label': '9C2', 'order': 9, 'powers': [21, 6], 'representative': 160, 'size': 4}
id: 139761197
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 21, 'group_counter': 295, 'group_order': 648, 'label': '9C4', 'order': 9, 'powers': [19, 6], 'representative': 320, 'size': 4}
id: 139761198
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 22, 'group_counter': 295, 'group_order': 648, 'label': '9D1', 'order': 9, 'powers': [23, 5], 'representative': 84, 'size': 4}
id: 139761199
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 23, 'group_counter': 295, 'group_order': 648, 'label': '9D2', 'order': 9, 'powers': [24, 5], 'representative': 168, 'size': 4}
id: 139761200
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 24, 'group_counter': 295, 'group_order': 648, 'label': '9D4', 'order': 9, 'powers': [22, 5], 'representative': 300, 'size': 4}
id: 139761201
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 25, 'group_counter': 295, 'group_order': 648, 'label': '9E1', 'order': 9, 'powers': [26, 6], 'representative': 512, 'size': 4}
id: 139761202
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 26, 'group_counter': 295, 'group_order': 648, 'label': '9E2', 'order': 9, 'powers': [27, 6], 'representative': 376, 'size': 4}
id: 139761203
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 27, 'group_counter': 295, 'group_order': 648, 'label': '9E4', 'order': 9, 'powers': [25, 6], 'representative': 104, 'size': 4}
id: 139761204
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 28, 'group_counter': 295, 'group_order': 648, 'label': '9F1', 'order': 9, 'powers': [29, 6], 'representative': 296, 'size': 4}
id: 139761205
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 29, 'group_counter': 295, 'group_order': 648, 'label': '9F2', 'order': 9, 'powers': [30, 6], 'representative': 592, 'size': 4}
id: 139761207
{'aut_label': '9A1', 'centralizer': '4.a1.a1', 'counter': 30, 'group_counter': 295, 'group_order': 648, 'label': '9F4', 'order': 9, 'powers': [28, 6], 'representative': 536, 'size': 4}
id: 139761208
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 31, 'group_counter': 295, 'group_order': 648, 'label': '18A1', 'order': 18, 'powers': [13, 11], 'representative': 36, 'size': 4}
id: 139761209
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 32, 'group_counter': 295, 'group_order': 648, 'label': '18A5', 'order': 18, 'powers': [15, 11], 'representative': 468, 'size': 4}
id: 139761210
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 33, 'group_counter': 295, 'group_order': 648, 'label': '18A7', 'order': 18, 'powers': [14, 11], 'representative': 252, 'size': 4}
id: 139761211
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 34, 'group_counter': 295, 'group_order': 648, 'label': '18B1', 'order': 18, 'powers': [16, 11], 'representative': 48, 'size': 4}
id: 139761212
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 35, 'group_counter': 295, 'group_order': 648, 'label': '18B5', 'order': 18, 'powers': [18, 11], 'representative': 480, 'size': 4}
id: 139761213
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 36, 'group_counter': 295, 'group_order': 648, 'label': '18B7', 'order': 18, 'powers': [17, 11], 'representative': 264, 'size': 4}
id: 139761214
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 37, 'group_counter': 295, 'group_order': 648, 'label': '18C1', 'order': 18, 'powers': [19, 12], 'representative': 40, 'size': 4}
id: 139761215
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 38, 'group_counter': 295, 'group_order': 648, 'label': '18C5', 'order': 18, 'powers': [21, 12], 'representative': 44, 'size': 4}
id: 139761216
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 39, 'group_counter': 295, 'group_order': 648, 'label': '18C7', 'order': 18, 'powers': [20, 12], 'representative': 184, 'size': 4}
id: 139761218
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 40, 'group_counter': 295, 'group_order': 648, 'label': '18D1', 'order': 18, 'powers': [22, 11], 'representative': 60, 'size': 4}
id: 139761219
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 41, 'group_counter': 295, 'group_order': 648, 'label': '18D5', 'order': 18, 'powers': [24, 11], 'representative': 192, 'size': 4}
id: 139761220
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 42, 'group_counter': 295, 'group_order': 648, 'label': '18D7', 'order': 18, 'powers': [23, 11], 'representative': 112, 'size': 4}
id: 139761221
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 43, 'group_counter': 295, 'group_order': 648, 'label': '18E1', 'order': 18, 'powers': [25, 12], 'representative': 256, 'size': 4}
id: 139761222
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 44, 'group_counter': 295, 'group_order': 648, 'label': '18E5', 'order': 18, 'powers': [27, 12], 'representative': 52, 'size': 4}
id: 139761223
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 45, 'group_counter': 295, 'group_order': 648, 'label': '18E7', 'order': 18, 'powers': [26, 12], 'representative': 476, 'size': 4}
id: 139761224
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 46, 'group_counter': 295, 'group_order': 648, 'label': '18F1', 'order': 18, 'powers': [28, 12], 'representative': 472, 'size': 4}
id: 139761225
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 47, 'group_counter': 295, 'group_order': 648, 'label': '18F5', 'order': 18, 'powers': [30, 12], 'representative': 68, 'size': 4}
id: 139761226
{'aut_label': '18A1', 'centralizer': '4.a1.a1', 'counter': 48, 'group_counter': 295, 'group_order': 648, 'label': '18F7', 'order': 18, 'powers': [29, 12], 'representative': 64, 'size': 4}

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: 12767430
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.1a', '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], 'schur_index': 1}
id: 12767441
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.1b', '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], 'schur_index': 1}
id: 12767445
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.1c', '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], 'schur_index': 1}
id: 12767446
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.1d', '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], 'schur_index': 1}
id: 12767447
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
id: 12767448
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
id: 12767449
{'cdim': 4, 'counter': 7, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4a', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, -2, 1, -2, -2, 1, -2, 1, 1, -2, 1, -2, -2, -2, 1, 1, 1, 1, -2, 1, -2, -2, -2, 1, -2, -2, 1, -2, -2, 1, -2, 1, 1, 1, -2, 1, 1], 'schur_index': 1}
id: 12767450
{'cdim': 4, 'counter': 8, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4b', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 1, -2, 1, 1, -2, 1, -2, -2, 1, -2, 1, 1, 1, -2, -2, -2, -2, 1, -2, 1, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, -2, -2, -2, 1, -2, -2], 'schur_index': 1}
id: 12767451
{'cdim': 4, 'counter': 9, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4c', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 0, 0, 0, 0, -4, -4, -2, 1, -2, -2, 1, -2, 1, 1, -2, 1, -2, -2, -2, 1, 1, 1, 1, -2, -1, 2, 2, 2, -1, 2, 2, -1, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
id: 12767431
{'cdim': 4, 'counter': 10, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4d', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 0, 0, 0, 0, -4, -4, 1, -2, 1, 1, -2, 1, -2, -2, 1, -2, 1, 1, 1, -2, -2, -2, -2, 1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, 2, 2, 2, -1, 2, 2], 'schur_index': 1}
id: 12767432
{'cdim': 4, 'counter': 11, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4e', 'multiplicity': 3, 'nt': [18, 130], 'qdim': 12, 'qvalues': [12, 12, 0, 0, -6, 3, 0, 0, 0, 0, -6, 3, 0, -3, 0, 0, -3, 0, -3, -3, 0, -3, 0, 0, 0, 6, 6, 6, -3, 0, -3, 0, 0, 0, 6, 0, 0, -3, 0, 0, -3, 0, -3, -3, -3, 0, 6, 6], 'schur_index': 1}
id: 12767433
{'cdim': 4, 'counter': 12, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4f', 'multiplicity': 3, 'nt': [18, 130], 'qdim': 12, 'qvalues': [12, 12, 0, 0, -6, 3, 0, 0, 0, 0, -6, 3, 0, -3, 0, 0, 6, 0, 6, -3, 0, -3, 0, 0, 0, -3, -3, -3, 6, 0, -3, 0, 0, 0, -3, 0, 0, 6, 0, 0, 6, 0, 6, -3, -3, 0, -3, -3], 'schur_index': 1}
id: 12767434
{'cdim': 4, 'counter': 13, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4g', 'multiplicity': 3, 'nt': [18, 130], 'qdim': 12, 'qvalues': [12, 12, 0, 0, -6, 3, 0, 0, 0, 0, -6, 3, 0, 6, 0, 0, -3, 0, -3, 6, 0, 6, 0, 0, 0, -3, -3, -3, -3, 0, 6, 0, 0, 0, -3, 0, 0, -3, 0, 0, -3, 0, -3, 6, 6, 0, -3, -3], 'schur_index': 1}
id: 12767435
{'cdim': 4, 'counter': 14, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4h', 'multiplicity': 3, 'nt': [18, 130], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 3, -6, 0, 0, 0, 0, 3, -6, -3, 0, -3, -3, 0, -3, 0, 0, 6, 0, -3, 6, 6, 0, 0, 0, 0, -3, 0, -3, -3, 6, 0, -3, -3, 0, 6, -3, 0, -3, 0, 0, 0, 6, 0, 0], 'schur_index': 1}
id: 12767436
{'cdim': 4, 'counter': 15, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4i', 'multiplicity': 3, 'nt': [18, 130], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 3, -6, 0, 0, 0, 0, 3, -6, -3, 0, 6, 6, 0, -3, 0, 0, -3, 0, -3, -3, -3, 0, 0, 0, 0, 6, 0, -3, 6, -3, 0, 6, -3, 0, -3, 6, 0, -3, 0, 0, 0, -3, 0, 0], 'schur_index': 1}
id: 12767437
{'cdim': 4, 'counter': 16, 'faithful': False, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4j', 'multiplicity': 3, 'nt': [18, 130], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 3, -6, 0, 0, 0, 0, 3, -6, 6, 0, -3, -3, 0, 6, 0, 0, -3, 0, 6, -3, -3, 0, 0, 0, 0, -3, 0, 6, -3, -3, 0, -3, 6, 0, -3, -3, 0, 6, 0, 0, 0, -3, 0, 0], 'schur_index': 1}
id: 12767438
{'cdim': 4, 'counter': 17, 'faithful': True, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4k', 'multiplicity': 3, 'nt': [36, 1035], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -6, 3, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, -3, 0, -3, -3, 0, -3, 0, 0, 0, 6, 6, 6, -3, 0, 3, 0, 0, 0, -6, 0, 0, 3, 0, 0, 3, 0, 3, 3, 3, 0, -6, -6], 'schur_index': 1}
id: 12767439
{'cdim': 4, 'counter': 18, 'faithful': True, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4l', 'multiplicity': 3, 'nt': [36, 1035], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -6, 3, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 6, 0, 6, -3, 0, -3, 0, 0, 0, -3, -3, -3, 6, 0, 3, 0, 0, 0, 3, 0, 0, -6, 0, 0, -6, 0, -6, 3, 3, 0, 3, 3], 'schur_index': 1}
id: 12767440
{'cdim': 4, 'counter': 19, 'faithful': True, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4m', 'multiplicity': 3, 'nt': [36, 1035], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -6, 3, 0, 0, 0, 0, 6, -3, 0, 6, 0, 0, -3, 0, -3, 6, 0, 6, 0, 0, 0, -3, -3, -3, -3, 0, -6, 0, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 3, -6, -6, 0, 3, 3], 'schur_index': 1}
id: 12767442
{'cdim': 4, 'counter': 20, 'faithful': True, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4n', 'multiplicity': 3, 'nt': [36, 1035], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 3, -6, 0, 0, 0, 0, -3, 6, -3, 0, -3, -3, 0, -3, 0, 0, 6, 0, -3, 6, 6, 0, 0, 0, 0, -3, 0, 3, 3, -6, 0, 3, 3, 0, -6, 3, 0, 3, 0, 0, 0, -6, 0, 0], 'schur_index': 1}
id: 12767443
{'cdim': 4, 'counter': 21, 'faithful': True, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4o', 'multiplicity': 3, 'nt': [36, 1035], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 3, -6, 0, 0, 0, 0, -3, 6, -3, 0, 6, 6, 0, -3, 0, 0, -3, 0, -3, -3, -3, 0, 0, 0, 0, 6, 0, 3, -6, 3, 0, -6, 3, 0, 3, -6, 0, 3, 0, 0, 0, 3, 0, 0], 'schur_index': 1}
id: 12767444
{'cdim': 4, 'counter': 22, 'faithful': True, 'group': '648.295', 'group_order': 648, 'image': None, 'label': '648.295.4p', 'multiplicity': 3, 'nt': [36, 1035], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 3, -6, 0, 0, 0, 0, -3, 6, 6, 0, -3, -3, 0, 6, 0, 0, -3, 0, 6, -3, -3, 0, 0, 0, 0, -3, 0, -6, 3, 3, 0, 3, -6, 0, 3, 3, 0, -6, 0, 0, 0, 3, 0, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 29511105
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 648, 'label': '648.295.1a', '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]]]}
id: 29511116
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 324, 'label': '648.295.1b', '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]]]}
id: 29511127
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 324, 'label': '648.295.1c', '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]]]}
id: 29511138
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 324, 'label': '648.295.1d', '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]]]}
id: 29511148
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 162, 'label': '648.295.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 29511149
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 162, 'label': '648.295.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 29511150
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id: 29511151
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id: 29511152
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id: 29511106
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id: 29511107
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id: 29511108
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id: 29511109
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id: 29511110
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id: 29511111
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id: 29511112
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id: 29511113
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id: 29511114
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id: 29511115
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id: 29511117
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id: 29511118
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id: 29511119
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id: 29511120
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 2, 'counter': 23, 'cyclotomic_n': 9, 'dim': 4, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '324.35', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 2, 'label': '648.295.4h2', 'nt': [18, 130], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 1], [-1, -1]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 4], [2, -4]], [[-1, 0], [1, 4], [1, -4]], [[2, 1], [2, -1]], [[-1, 4], [-1, -4]], [[2, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [-1, -2]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 0], [1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[-1, 0], [1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 0], [1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 2], [2, -2]], [[2, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 1], [2, -1]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 4], [2, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[2, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]]]}
id: 29511121
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id: 29511122
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id: 29511123
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id: 29511124
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id: 29511125
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id: 29511126
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id: 29511128
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id: 29511129
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id: 29511130
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id: 29511131
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id: 29511132
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id: 29511133
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id: 29511134
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id: 29511135
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id: 29511136
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id: 29511137
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id: 29511139
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id: 29511140
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id: 29511141
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id: 29511142
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id: 29511143
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id: 29511144
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 2, 'counter': 45, 'cyclotomic_n': 9, 'dim': 4, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '648.295', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.295.4o3', 'nt': [36, 1035], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 4], [-1, -4]], [[2, 0], [1, 4], [1, -4]], [[2, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[-1, 1], [-1, -1]], [[2, 0], [-1, 1], [1, 2], [-1, 4]], [[1, 1], [1, -1]], [[1, 0], [1, 1], [-1, 2], [1, 4]], [[-2, 0], [-1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [1, 4]], [[-2, 4], [-2, -4]], [[-2, 0], [1, 1], [-1, 2], [1, 4]], [[1, 0], [-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 0], [-1, 1], [1, 2], [1, -4]], [[-2, 0], [-1, 1], [1, 2], [1, -4]], [[1, 4], [1, -4]], [[1, 0], [-1, 1], [1, 2], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 0], [-1, 4], [-1, -4]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]]]}
id: 29511145
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 2, 'counter': 46, 'cyclotomic_n': 9, 'dim': 4, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '648.295', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.295.4p1', 'nt': [36, 1035], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0], [1, 4], [1, -4]], [[2, 2], [2, -2]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[2, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-1, -2]], [[2, 1], [2, -1]], [[-1, 0], [1, 4], [1, -4]], [[2, 4], [2, -4]], [[2, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[-2, 4], [-2, -4]], [[-2, 0], [-1, 1], [1, 2], [1, -4]], [[1, 0], [1, 1], [-1, 2], [1, 4]], [[1, 0], [-1, 1], [1, 2], [1, -4]], [[1, 2], [1, -2]], [[1, 0], [-1, 1], [1, 2], [1, -4]], [[-2, 0], [1, 1], [-1, 2], [1, 4]], [[1, 4], [1, -4]], [[1, 0], [-1, 4], [-1, -4]], [[1, 0], [-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-2, 0], [-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[1, 0], [1, 1], [-1, 2], [1, 4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]]]}
id: 29511146
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 2, 'counter': 47, 'cyclotomic_n': 9, 'dim': 4, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '648.295', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.295.4p2', 'nt': [36, 1035], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 1], [2, -1]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 4], [-1, -4]], [[2, 0], [1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[2, 4], [2, -4]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[2, 2], [2, -2]], [[2, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 0], [1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 0], [1, 4], [1, -4]], [[-2, 2], [-2, -2]], [[-2, 0], [-1, 4], [-1, -4]], [[1, 0], [-1, 1], [1, 2], [1, -4]], [[1, 0], [-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 0], [-1, 4], [-1, -4]], [[-2, 0], [-1, 1], [1, 2], [1, -4]], [[1, 2], [1, -2]], [[1, 0], [1, 1], [-1, 2], [1, 4]], [[1, 0], [1, 1], [-1, 2], [1, 4]], [[1, 1], [1, -1]], [[-2, 0], [1, 1], [-1, 2], [1, 4]], [[1, 4], [1, -4]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[1, 0], [-1, 1], [1, 2], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]]]}
id: 29511147
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 2, 'counter': 48, 'cyclotomic_n': 9, 'dim': 4, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '648.295', 'group_counter': 295, 'group_order': 648, 'image': None, 'image_isoclass': '648.295', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.295.4p3', 'nt': [36, 1035], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 4], [2, -4]], [[-1, 0], [1, 4], [1, -4]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[-1, 2], [-1, -2]], [[2, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 4], [-1, -4]], [[2, 2], [2, -2]], [[-1, 0], [1, 1], [-1, 2], [-1, -4]], [[2, 1], [2, -1]], [[2, 0], [1, 4], [1, -4]], [[-1, 0], [1, 4], [1, -4]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 0], [-1, 1], [1, 2], [-1, 4]], [[-2, 1], [-2, -1]], [[-2, 0], [1, 1], [-1, 2], [1, 4]], [[1, 0], [-1, 4], [-1, -4]], [[1, 0], [1, 1], [-1, 2], [1, 4]], [[1, 4], [1, -4]], [[1, 0], [1, 1], [-1, 2], [1, 4]], [[-2, 0], [-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 0], [-1, 1], [1, 2], [1, -4]], [[1, 0], [-1, 1], [1, 2], [1, -4]], [[1, 4], [1, -4]], [[-2, 0], [-1, 1], [1, 2], [1, -4]], [[1, 2], [1, -2]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[1, 0], [-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}

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

gps_subgroup_search • Show schema

id: 110362490
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '648.295.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.295', 'subgroup_hash': 295, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_9^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 110362501
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.295.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.74', 'subgroup_hash': 74, 'subgroup_order': 324, 'subgroup_tex': 'C_9:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362512
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '648.295.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.35', 'subgroup_hash': 35, 'subgroup_order': 324, 'subgroup_tex': 'C_9^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 110362523
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '648.295.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.35', 'subgroup_hash': 35, 'subgroup_order': 324, 'subgroup_tex': 'C_9^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 110362534
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 162, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.295.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.23', 'subgroup_hash': 23, 'subgroup_order': 162, 'subgroup_tex': 'C_9\\times C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362545
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 162, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.295.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.16', 'subgroup_hash': 16, 'subgroup_order': 162, 'subgroup_tex': 'C_9:D_9', 'supersolvable': True, 'sylow': 0}
id: 110362556
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 162, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.295.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.16', 'subgroup_hash': 16, 'subgroup_order': 162, 'subgroup_tex': 'C_9:D_9', 'supersolvable': True, 'sylow': 0}
id: 110362562
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362563
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362491
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 81, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '648.295.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.2', 'subgroup_hash': 2, 'subgroup_order': 81, 'subgroup_tex': 'C_9^2', 'supersolvable': True, 'sylow': 3}
id: 110362492
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 110362493
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362494
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362495
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
id: 110362496
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
id: 110362497
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
id: 110362498
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
id: 110362499
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362500
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362502
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362503
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362504
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.a1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362505
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.a1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362506
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
id: 110362507
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 110362508
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 110362509
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 110362510
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
id: 110362511
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 18, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.295.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 110362513
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362514
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.36.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362515
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.36.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362516
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.36.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362517
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.36.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362518
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.36.b1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 110362519
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362520
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362521
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362522
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362524
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.c1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362525
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.c1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362526
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 110362527
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362528
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362529
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362530
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362531
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.e1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362532
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.e1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 110362533
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 110362535
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 110362536
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.54.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 110362537
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 9, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.295.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 110362538
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 110362539
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.72.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 110362540
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.72.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 110362541
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.72.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 110362542
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.72.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 110362543
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.72.b1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 110362544
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '648.295.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 2}
id: 110362546
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 110362547
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.108.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 110362548
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 110362549
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.108.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 110362550
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 110362551
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.108.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 110362552
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.295.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 110362553
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 110362554
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.162.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 110362555
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 110362557
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.216.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 110362558
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 2, 'counter': 71, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '648.295.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '324.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '324.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_9^2:C_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 110362559
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 110362560
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.295.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 110362561
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.295', 'ambient_counter': 295, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_9^2:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 1, 'counter': 74, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '648.295.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '648.295', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 295, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_9^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

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

gps_subgroup_data • Show schema

id: 110362490
{'ambient': '648.295', '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': '324.a1.a1', 'complements': ['648.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7408, 3467, 8840, 3751, 5957, 3228, 5959, 3543], 'generators': [1, 444, 504, 324, 216, 2, 376], 'label': '648.295.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '324.35'}
id: 110362491
{'ambient': '648.295', 'aut_centralizer_order': 162, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.71', 'aut_weyl_index': 162, 'centralizer': '4.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['24.a1.a1', '24.a1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2822, 4971, 5213, 6017, 376, 4739, 4427, 5773], 'generators': [580, 288], 'label': '648.295.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '648.295', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 110362492
{'ambient': '648.295', 'aut_centralizer_order': 9, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 81, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['18.b1.a1', '18.c1.a1', '18.c1.b1', '81.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8830, -1, 9638, -1, 8269, -1, 8297, -1], 'generators': [1, 216, 324, 2, 444], 'label': '648.295.9.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 110362493
{'ambient': '648.295', 'aut_centralizer_order': 162, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.b1.a1', '36.b1.b1', '36.b1.c1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4392, -1, 6329, -1, 2825, -1, 2798, -1], 'generators': [324, 288, 444, 216], 'label': '648.295.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362494
{'ambient': '648.295', 'aut_centralizer_order': 162, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.b1'], 'contains': ['24.a1.b1', '36.a1.a1', '36.b1.d1', '36.b1.e1', '36.b1.f1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4392, -1, 2876, -1, 2825, -1, 6095, -1], 'generators': [324, 580, 216, 444], 'label': '648.295.12.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362495
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 24, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '36.c1.a1', '36.c1.b1', '36.c1.c1', '36.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5860, -1, 8243, -1, 4283, -1, 3358, -1], 'generators': [2, 504, 444, 216], 'label': '648.295.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.7'}
id: 110362496
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 24, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.b1'], 'contains': ['24.a1.b1', '36.c1.d1', '36.c1.e1', '36.c1.f1', '36.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5860, -1, 3877, -1, 4283, -1, 7434, -1], 'generators': [2, 376, 216, 444], 'label': '648.295.12.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '12.b1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '54.7'}
id: 110362497
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 24, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '36.e1.a1', '36.e1.b1', '36.e1.c1', '36.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2442, -1, 4581, -1, 1367, -1, 2237, -1], 'generators': [326, 504, 444, 216], 'label': '648.295.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.7'}
id: 110362498
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 24, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.b1'], 'contains': ['24.a1.b1', '36.e1.d1', '36.e1.e1', '36.e1.f1', '36.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2442, -1, 2234, -1, 1367, -1, 5534, -1], 'generators': [326, 376, 216, 444], 'label': '648.295.12.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '12.c1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '54.7'}
id: 110362499
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.e1.a1', '54.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1388, -1, 7018, -1, 5319, -1, 1834, -1], 'generators': [324, 2, 288, 216], 'label': '648.295.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362500
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['36.b1.b1', '36.c1.b1', '36.e1.b1', '54.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1388, -1, 7363, -1, 5319, -1, 1134, -1], 'generators': [324, 2, 528, 216], 'label': '648.295.18.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '18.a1.b1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362501
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '11664.lk', 'aut_weyl_index': 2, 'centralizer': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1', '6.a1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5758, 5531, 5457, 7021, 3838, 5151, 5149, 6634], 'generators': [324, 216, 444, 2, 376, 504], 'label': '648.295.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '324.35'}
id: 110362502
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['36.b1.c1', '36.c1.c1', '36.e1.c1', '54.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1388, -1, 7801, -1, 5319, -1, 3757, -1], 'generators': [324, 2, 84, 216], 'label': '648.295.18.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.c1', 'old_label': '18.a1.c1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.c1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362503
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1'], 'contains': ['36.b1.d1', '36.c1.d1', '36.e1.d1', '54.a1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1388, -1, 138, -1, 5319, -1, 7036, -1], 'generators': [324, 2, 364, 444], 'label': '648.295.18.a1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.d1', 'old_label': '18.a1.d1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.d1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362504
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1'], 'contains': ['36.b1.e1', '36.c1.e1', '36.e1.e1', '54.a1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1388, -1, 2408, -1, 5319, -1, 7833, -1], 'generators': [324, 2, 580, 444], 'label': '648.295.18.a1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.e1', 'old_label': '18.a1.e1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.e1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362505
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1'], 'contains': ['36.b1.f1', '36.c1.f1', '36.e1.f1', '54.a1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1388, -1, 657, -1, 5319, -1, 6646, -1], 'generators': [324, 2, 148, 444], 'label': '648.295.18.a1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.f1', 'old_label': '18.a1.f1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.f1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362506
{'ambient': '648.295', 'aut_centralizer_order': 18, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 162, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.a1.b1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.d1.a1', '36.f1.a1', '54.a1.a1', '54.a1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6606, -1, 5344, -1, 6777, -1, 4969, -1], 'generators': [324, 2, 444, 216], 'label': '648.295.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 110362507
{'ambient': '648.295', 'aut_centralizer_order': 9, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.182', 'aut_weyl_index': 162, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '162.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8694, -1, 9638, -1, 8417, -1, 8297, -1], 'generators': [1, 2, 444, 216], 'label': '648.295.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 110362508
{'ambient': '648.295', 'aut_centralizer_order': 9, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.182', 'aut_weyl_index': 162, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '9.a1.a1'], 'contains': ['36.d1.a1', '162.b1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8694, -1, 9165, -1, 8417, -1, 8998, -1], 'generators': [325, 2, 444, 216], 'label': '648.295.18.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 110362509
{'ambient': '648.295', 'aut_centralizer_order': 162, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.b1.b1', '72.b1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3956, -1, 5403, -1, 672, -1, 2290, -1], 'generators': [288, 444], 'label': '648.295.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362510
{'ambient': '648.295', 'aut_centralizer_order': 162, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.b1', '12.b1.b1', '12.c1.b1'], 'contains': ['72.a1.a1', '72.b1.d1', '72.b1.e1', '72.b1.f1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3956, -1, 3140, -1, 672, -1, 5530, -1], 'generators': [580, 216], 'label': '648.295.24.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362511
{'ambient': '648.295', 'aut_centralizer_order': 1458, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.8', 'aut_weyl_index': 1458, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.a1.b1', '18.b1.a1'], 'contains': ['72.a1.a1', '108.a1.a1', '108.a1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6640, 7921, 4462, 8352, 5911, 7871, 4619, 8289], 'generators': [324, 444, 216], 'label': '648.295.36.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['72.a1.a1', '324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '324.35', 'quotient_action_image': '4.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 110362512
{'ambient': '648.295', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '11664.lk', 'aut_weyl_index': 2, 'centralizer': '324.a1.a1', 'complements': ['324.a1.a1', '324.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '18.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7408, 1401, 9056, 1110, 5957, 1305, 5793, 1049], 'generators': [1, 216, 444, 2, 376, 504], 'label': '648.295.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '648.295', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.35'}
id: 110362513
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '108.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1227, -1, 5894, -1, 2768, -1, 1484, -1], 'generators': [324, 72, 216], 'label': '648.295.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362514
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.b1'], 'contains': ['72.b1.b1', '108.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1227, -1, 6662, -1, 2768, -1, 784, -1], 'generators': [324, 312, 216], 'label': '648.295.36.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.b1.b1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362515
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.c1'], 'contains': ['72.b1.c1', '108.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1227, -1, 7150, -1, 2768, -1, 3411, -1], 'generators': [324, 516, 216], 'label': '648.295.36.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.b1.c1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362516
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '18.a1.d1'], 'contains': ['72.b1.d1', '108.a1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1227, -1, 1137, -1, 2768, -1, 7439, -1], 'generators': [324, 604, 444], 'label': '648.295.36.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.b1.d1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362517
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '18.a1.e1'], 'contains': ['72.b1.e1', '108.a1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1227, -1, 3098, -1, 2768, -1, 8770, -1], 'generators': [324, 172, 444], 'label': '648.295.36.b1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.b1.e1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362518
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '18.a1.f1'], 'contains': ['72.b1.f1', '108.a1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1227, -1, 1757, -1, 2768, -1, 6651, -1], 'generators': [324, 388, 444], 'label': '648.295.36.b1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.b1.f1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362519
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '108.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': '36T1035', 'count': 18, 'diagramx': [3303, -1, 7607, -1, 4727, -1, 1834, -1], 'generators': [2, 288, 216], 'label': '648.295.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362520
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.b1'], 'contains': ['72.b1.b1', '108.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': '36T1035', 'count': 18, 'diagramx': [3303, -1, 8033, -1, 4727, -1, 1134, -1], 'generators': [2, 528, 216], 'label': '648.295.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.c1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362521
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.c1'], 'contains': ['72.b1.c1', '108.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': '36T1035', 'count': 18, 'diagramx': [3303, -1, 8816, -1, 4727, -1, 3761, -1], 'generators': [2, 84, 216], 'label': '648.295.36.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.c1', 'old_label': '36.c1.c1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.c1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362522
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '18.a1.d1'], 'contains': ['72.b1.d1', '108.b1.b1'], 'core': '648.a1.a1', 'coset_action_label': '36T1035', 'count': 18, 'diagramx': [3303, -1, 1447, -1, 4727, -1, 8419, -1], 'generators': [2, 364, 444], 'label': '648.295.36.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.d1', 'old_label': '36.c1.d1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.d1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362523
{'ambient': '648.295', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '11664.lk', 'aut_weyl_index': 2, 'centralizer': '324.a1.a1', 'complements': ['324.a1.a1', '324.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '18.c1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7408, 1401, 8618, 3751, 5957, 1305, 6458, 3543], 'generators': [325, 216, 444, 2, 376, 504], 'label': '648.295.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '648.295', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '324.35'}
id: 110362524
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '18.a1.e1'], 'contains': ['72.b1.e1', '108.b1.b1'], 'core': '648.a1.a1', 'coset_action_label': '36T1035', 'count': 18, 'diagramx': [3303, -1, 3554, -1, 4727, -1, 9120, -1], 'generators': [2, 580, 444], 'label': '648.295.36.c1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.e1', 'old_label': '36.c1.e1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.e1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362525
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '18.a1.f1'], 'contains': ['72.b1.f1', '108.b1.b1'], 'core': '648.a1.a1', 'coset_action_label': '36T1035', 'count': 18, 'diagramx': [3303, -1, 2787, -1, 4727, -1, 8104, -1], 'generators': [2, 148, 444], 'label': '648.295.36.c1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.f1', 'old_label': '36.c1.f1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.f1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362526
{'ambient': '648.295', 'aut_centralizer_order': 18, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 162, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.b1.b1', '18.b1.a1', '18.c1.a1', '18.c1.b1'], 'contains': ['72.a1.a1', '108.b1.a1', '108.b1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7948, -1, 8498, -1, 7210, -1, 7045, -1], 'generators': [2, 444, 216], 'label': '648.295.36.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 110362527
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '108.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': '36T1036', 'count': 18, 'diagramx': [309, -1, 5012, -1, 1857, -1, 433, -1], 'generators': [326, 288, 216], 'label': '648.295.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362528
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.b1'], 'contains': ['72.b1.b1', '108.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': '36T1036', 'count': 18, 'diagramx': [309, -1, 5438, -1, 1857, -1, 118, -1], 'generators': [326, 528, 216], 'label': '648.295.36.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.e1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362529
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.c1'], 'contains': ['72.b1.c1', '108.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': '36T1036', 'count': 18, 'diagramx': [309, -1, 6352, -1, 1857, -1, 2745, -1], 'generators': [326, 84, 216], 'label': '648.295.36.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.c1', 'old_label': '36.e1.c1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.c1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362530
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '18.a1.d1'], 'contains': ['72.b1.d1', '108.c1.b1'], 'core': '648.a1.a1', 'coset_action_label': '36T1036', 'count': 18, 'diagramx': [309, -1, 253, -1, 1857, -1, 5985, -1], 'generators': [326, 364, 444], 'label': '648.295.36.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.d1', 'old_label': '36.e1.d1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.d1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362531
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '18.a1.e1'], 'contains': ['72.b1.e1', '108.c1.b1'], 'core': '648.a1.a1', 'coset_action_label': '36T1036', 'count': 18, 'diagramx': [309, -1, 2214, -1, 1857, -1, 6300, -1], 'generators': [326, 580, 444], 'label': '648.295.36.e1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.e1', 'old_label': '36.e1.e1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.e1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362532
{'ambient': '648.295', 'aut_centralizer_order': 4, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '18.a1.f1'], 'contains': ['72.b1.f1', '108.c1.b1'], 'core': '648.a1.a1', 'coset_action_label': '36T1036', 'count': 18, 'diagramx': [309, -1, 680, -1, 1857, -1, 5074, -1], 'generators': [326, 148, 444], 'label': '648.295.36.e1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.f1', 'old_label': '36.e1.f1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.f1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 110362533
{'ambient': '648.295', 'aut_centralizer_order': 18, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 162, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.c1.b1', '18.b1.a1'], 'contains': ['72.a1.a1', '108.c1.a1', '108.c1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4324, -1, 4020, -1, 3793, -1, 4120, -1], 'generators': [326, 444, 216], 'label': '648.295.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 110362534
{'ambient': '648.295', 'aut_centralizer_order': 162, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.71', 'aut_weyl_index': 162, 'centralizer': '4.a1.a1', 'complements': ['162.b1.a1', '162.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.a1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4163, 8599, 5340, 8890, 2381, 8008, 5088, 8399], 'generators': [324, 216, 580, 288, 444], 'label': '648.295.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '324.35', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 110362535
{'ambient': '648.295', 'aut_centralizer_order': 36, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.a1.b1', '18.a1.c1', '18.b1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '162.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4301, -1, 7661, -1, 8144, -1, 3060, -1], 'generators': [324, 2, 216], 'label': '648.295.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 110362536
{'ambient': '648.295', 'aut_centralizer_order': 36, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.d1', '18.a1.e1', '18.a1.f1', '18.b1.a1'], 'contains': ['108.a1.b1', '108.b1.b1', '108.c1.b1', '162.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4301, -1, 758, -1, 8144, -1, 7789, -1], 'generators': [324, 2, 444], 'label': '648.295.54.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.b1', 'old_label': '54.a1.b1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 110362537
{'ambient': '648.295', 'aut_centralizer_order': 1458, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.8', 'aut_weyl_index': 1458, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.a1.b1', '36.a1.a1', '36.d1.a1', '36.f1.a1'], 'contains': ['216.a1.a1', '216.a1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6686, 6151, 4504, 6951, 4693, 5755, 4619, 6589], 'generators': [444, 216], 'label': '648.295.72.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['8.a1.a1', '36.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '648.295', 'quotient_action_image': '4.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 110362538
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.b1.a1', '36.c1.a1', '36.e1.a1'], 'contains': ['216.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1926, -1, 5174, -1, 2768, -1, 1834, -1], 'generators': [72], 'label': '648.295.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362539
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.b1.b1', '36.c1.b1', '36.e1.b1'], 'contains': ['216.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1926, -1, 6205, -1, 2768, -1, 1134, -1], 'generators': [312], 'label': '648.295.72.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.b1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362540
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.b1.c1', '36.c1.c1', '36.e1.c1'], 'contains': ['216.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1926, -1, 6933, -1, 2768, -1, 3393, -1], 'generators': [516], 'label': '648.295.72.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.b1.c1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362541
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '36.b1.d1', '36.c1.d1', '36.e1.d1'], 'contains': ['216.a1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1926, -1, 1641, -1, 2768, -1, 6616, -1], 'generators': [604], 'label': '648.295.72.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.b1.d1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362542
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '36.b1.e1', '36.c1.e1', '36.e1.e1'], 'contains': ['216.a1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1926, -1, 3327, -1, 2768, -1, 7605, -1], 'generators': [172], 'label': '648.295.72.b1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.b1.e1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362543
{'ambient': '648.295', 'aut_centralizer_order': 324, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '36.b1.f1', '36.c1.f1', '36.e1.f1'], 'contains': ['216.a1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1926, -1, 2443, -1, 2768, -1, 6300, -1], 'generators': [388], 'label': '648.295.72.b1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.b1.f1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362544
{'ambient': '648.295', 'aut_centralizer_order': 72, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['162.a1.a1', '162.b1.a1', '162.b1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9691, -1, 9757, -1, 9328, -1, 9742, -1], 'generators': [1, 324], 'label': '648.295.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 110362545
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '11664.lk', 'aut_weyl_index': 2, 'centralizer': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '12.b1.a1', '12.b1.b1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6606, 2109, 7534, 3751, 3838, 1964, 5723, 3543], 'generators': [2, 216, 376, 504, 444], 'label': '648.295.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.35'}
id: 110362546
{'ambient': '648.295', 'aut_centralizer_order': 2916, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.b1.b1', '36.b1.c1', '54.a1.a1'], 'contains': ['216.a1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3670, -1, 6859, -1, 6390, -1, 3078, -1], 'generators': [324, 216], 'label': '648.295.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362547
{'ambient': '648.295', 'aut_centralizer_order': 2916, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.d1', '36.b1.e1', '36.b1.f1', '54.a1.b1'], 'contains': ['216.a1.b1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3670, -1, 2001, -1, 6390, -1, 6931, -1], 'generators': [324, 444], 'label': '648.295.108.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '108.a1.b1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362548
{'ambient': '648.295', 'aut_centralizer_order': 36, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.c1.b1', '36.c1.c1', '36.d1.a1', '54.a1.a1'], 'contains': ['216.a1.a1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4931, -1, 8176, -1, 7210, -1, 3708, -1], 'generators': [2, 216], 'label': '648.295.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 110362549
{'ambient': '648.295', 'aut_centralizer_order': 36, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.d1', '36.c1.e1', '36.c1.f1', '36.d1.a1', '54.a1.b1'], 'contains': ['216.a1.b1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4931, -1, 3032, -1, 7210, -1, 7920, -1], 'generators': [2, 444], 'label': '648.295.108.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.b1', 'old_label': '108.b1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 110362550
{'ambient': '648.295', 'aut_centralizer_order': 36, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.e1.b1', '36.e1.c1', '36.f1.a1', '54.a1.a1'], 'contains': ['216.a1.a1', '324.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2753, -1, 5387, -1, 5570, -1, 2763, -1], 'generators': [326, 216], 'label': '648.295.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 110362551
{'ambient': '648.295', 'aut_centralizer_order': 36, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.d1', '36.e1.e1', '36.e1.f1', '36.f1.a1', '54.a1.b1'], 'contains': ['216.a1.b1', '324.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2753, -1, 1052, -1, 5570, -1, 5985, -1], 'generators': [326, 444], 'label': '648.295.108.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.b1', 'old_label': '108.c1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 110362552
{'ambient': '648.295', 'aut_centralizer_order': 288, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 23328, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.a1.b1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.b1.a1', '324.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5860, -1, 7724, -1, 8087, -1, 7268, -1], 'generators': [324, 2], 'label': '648.295.162.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 110362553
{'ambient': '648.295', 'aut_centralizer_order': 72, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '81.a1.a1'], 'contains': ['324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8694, -1, 9862, -1, 9328, -1, 9361, -1], 'generators': [1], 'label': '648.295.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 110362554
{'ambient': '648.295', 'aut_centralizer_order': 72, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '81.a1.a1'], 'contains': ['324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8694, -1, 9420, -1, 9328, -1, 9742, -1], 'generators': [325], 'label': '648.295.162.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.b1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 110362555
{'ambient': '648.295', 'aut_centralizer_order': 2916, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.b1.b1', '72.b1.c1', '108.a1.a1', '108.b1.a1', '108.c1.a1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2798, -1, 6271, -1, 5592, -1, 3236, -1], 'generators': [216], 'label': '648.295.216.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362556
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '11664.lk', 'aut_weyl_index': 2, 'centralizer': '324.a1.a1', 'complements': ['162.b1.a1', '162.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.c1.a1', '12.c1.b1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2696, 4822, 4736, 5899, 923, 4492, 4474, 5574], 'generators': [326, 216, 376, 504, 444], 'label': '648.295.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '648.295', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.35'}
id: 110362557
{'ambient': '648.295', 'aut_centralizer_order': 2916, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.d1', '72.b1.e1', '72.b1.f1', '108.a1.b1', '108.b1.b1', '108.c1.b1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2798, -1, 2845, -1, 5592, -1, 6616, -1], 'generators': [444], 'label': '648.295.216.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.a1.b1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 110362558
{'ambient': '648.295', 'aut_centralizer_order': 23328, 'aut_label': '324.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 23328, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.a1.b1', '162.a1.a1'], 'contains': ['648.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4324, 7862, 6669, 8307, 7244, 7871, 6300, 8289], 'generators': [324], 'label': '648.295.324.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': ['36.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '324.35', 'quotient_action_image': '1.1', 'quotient_action_kernel': '324.35', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 110362559
{'ambient': '648.295', 'aut_centralizer_order': 288, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 23328, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.b1.b1', '162.a1.a1', '162.b1.a1', '162.b1.b1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5390, -1, 8045, -1, 8075, -1, 7592, -1], 'generators': [2], 'label': '648.295.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 110362560
{'ambient': '648.295', 'aut_centralizer_order': 288, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 23328, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.c1.b1', '162.a1.a1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3062, -1, 5283, -1, 6424, -1, 5985, -1], 'generators': [326], 'label': '648.295.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.c1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 110362561
{'ambient': '648.295', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.a1.b1', '324.a1.a1', '324.b1.a1', '324.c1.a1'], 'contains': [], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4014, 7036, 6271, 7652, 6834, 6799, 6300, 7428], 'generators': [], 'label': '648.295.648.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['72.a1.a1', '324.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '648.295', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 110362562
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 24, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '18.a1.a1', '18.a1.b1', '18.a1.c1', '18.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5758, -1, 6743, -1, 5319, -1, 3078, -1], 'generators': [324, 216, 2, 504, 444], 'label': '648.295.6.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.7'}
id: 110362563
{'ambient': '648.295', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 24, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.b1', '12.b1.b1', '12.c1.b1', '18.a1.d1', '18.a1.e1', '18.a1.f1', '18.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5758, -1, 2617, -1, 5319, -1, 6410, -1], 'generators': [324, 444, 2, 376, 216], 'label': '648.295.6.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '6.a1.b1', 'projective_image': '324.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '54.7'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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