LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-18T06:11:23.988569

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [6, 6, 6, 12, 6, 18], 'aut_gens': [[1, 2, 12, 108], [329, 998, 528, 1224], [1197, 1222, 960, 828], [1, 238, 60, 144], [473, 134, 456, 576], [149, 170, 528, 1224], [973, 310, 12, 1260]], 'aut_group': None, 'aut_hash': 7842112311458244433, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 15552, 'aut_permdeg': 144, 'aut_perms': [2543582445884174289628344927941408591984656830918083515907966818917736556890337252277396480479131281509158010778320156934852474451555772197325981797330249951832538684700452246712478364014788269983100724039588318007276689940576612727582728534060553037, 1521462791332040460973460044838325251394649386844896754128301063204659423047818613493789103665663260414940153254871737078657343708345533689820385681165357142526935864644770606862395699339655325654354886153063783918359117955429021889538738378992753933, 1426525458197680005450991505783852698560107933813999793150918239327437387129344974481790726358052175937245064152632013816673766235602888045714494365782047520112007223294085846926087242279186228648654314301941721218651507287075098982006618549603899857, 726757934388021033781344421753203425078625530009956351872207363051824456764192885101166452454216738591530627204166756995842650910861610167337664665722830318401966687402259700174982020656323039543150154462124570872353419738163247658219629705359377917, 4709698142089195821244523382531955329136691865972253473355972225769846234832485682333542026205354487619921313089631060722320177948364622565668375845607820348352850086703630237957078996396753672471914755109106957904564980323147678797327247764322200808, 4522180381407743540157819907615439598207455304340196036810884603726332373990183089422520278418313928448686971933961025902692799531312725357491901770961765894775390751368363445074365185261547918176223494399940721970864348484462061373733789612948454797], 'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 108, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 18, 1, 1], [4, 2, 1, 1], [4, 108, 1, 1], [6, 2, 1, 1], [6, 6, 1, 1], [6, 18, 1, 1], [6, 108, 2, 1], [8, 18, 2, 1], [9, 6, 3, 1], [9, 36, 1, 1], [12, 2, 2, 1], [12, 12, 1, 1], [12, 36, 1, 1], [12, 108, 2, 1], [18, 6, 3, 1], [18, 36, 1, 1], [24, 18, 4, 1], [36, 6, 6, 1], [36, 36, 2, 1], [72, 18, 12, 1]], 'aut_supersolvable': True, 'aut_tex': '\\He_3.C_6^2.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': None, 'autcentquo_hash': 9022011127908065638, 'autcentquo_nilpotent': False, 'autcentquo_order': 3888, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times \\He_3.(C_6\\times S_3).C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 108, 1], [3, 2, 1], [3, 6, 1], [3, 18, 1], [4, 2, 1], [4, 108, 1], [6, 2, 1], [6, 6, 1], [6, 18, 1], [6, 108, 2], [8, 18, 2], [9, 6, 3], [9, 36, 1], [12, 2, 2], [12, 12, 1], [12, 36, 1], [12, 108, 2], [18, 6, 3], [18, 36, 1], [24, 18, 4], [36, 6, 6], [36, 36, 2], [72, 18, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '648.77', 'commutator_count': 1, 'commutator_label': '324.32', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 157, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 108, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 18, 1, 1], [4, 2, 1, 1], [4, 108, 1, 1], [6, 2, 1, 1], [6, 6, 1, 1], [6, 18, 1, 1], [6, 108, 2, 1], [8, 18, 2, 1], [9, 6, 3, 1], [9, 36, 1, 1], [12, 2, 2, 1], [12, 12, 1, 1], [12, 36, 1, 1], [12, 108, 2, 1], [18, 6, 3, 1], [18, 36, 1, 1], [24, 18, 4, 1], [36, 6, 6, 1], [36, 36, 2, 1], [72, 18, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 18, 'exponent': 72, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 12]], 'familial': False, 'frattini_label': '36.8', 'frattini_quotient': '36.10', 'hash': 157, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [4, 6, 9, 6], 'inner_gens': [[1, 982, 12, 612], [329, 2, 528, 1224], [1, 890, 12, 108], [901, 290, 12, 108]], 'inner_hash': 77, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': True, 'inner_tex': '\\He_3.D_{12}', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 72, 'irrQ_dim': 72, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 15], [4, 5], [6, 28], [12, 1]], 'label': '1296.157', 'linC_count': 12, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 22, 'linQ_degree_count': 4, 'linQ_dim': 22, 'linQ_dim_count': 2, 'linR_count': 36, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C3*C36).D6', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 53, 'number_divisions': 25, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 110, 'number_subgroup_classes': 112, 'number_subgroups': 1532, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 109], [3, 26], [4, 110], [6, 242], [8, 36], [9, 54], [12, 268], [18, 54], [24, 72], [36, 108], [72, 216]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 4, 0], 'outer_gens': [[1, 10, 12, 612], [5, 2, 528, 576], [657, 10, 444, 576]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [40320, 24, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 6], [6, 2], [8, 2], [12, 2], [18, 2], [36, 1], [72, 1]], 'representations': {'PC': {'code': 11246853459071453011879508999372428306981823831851067782203237673331513, 'gens': [1, 2, 4, 6], 'pres': [8, 2, 2, 3, 3, 3, 2, 2, 3, 2592, 15713, 41, 194, 8459, 3859, 123, 1452, 29381, 29389, 1749, 141, 62502, 32270, 4054, 166, 59911, 28815, 7511]}, 'Perm': {'d': 35, 'gens': [1595507918780023409480998742999311492, 35004891930892091089027449612236934057, 12568, 18498, 331891542554654683874677120817819846400, 636055220606841957361449674060960256000, 940191167853084406160007526694245171200, 1235663030766837015331996060090564894080]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_3\\times C_{36}).D_6', 'transitive_degree': 216, '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: 114460716
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 157, 'group_order': 1296, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 114460727
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 157, 'group_order': 1296, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 648, 'size': 1}
id: 114460738
{'aut_label': '2B', 'centralizer': '108.b1.a1', 'counter': 3, 'group_counter': 157, 'group_order': 1296, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 186, 'size': 108}
id: 114460749
{'aut_label': '3A', 'centralizer': '2.c1.a1', 'counter': 4, 'group_counter': 157, 'group_order': 1296, 'label': '3A', 'order': 3, 'powers': [4, 1], 'representative': 72, 'size': 2}
id: 114460760
{'aut_label': '3B', 'centralizer': '6.e1.a1', 'counter': 5, 'group_counter': 157, 'group_order': 1296, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 432, 'size': 6}
id: 114460765
{'aut_label': '3C', 'centralizer': '18.a1.a1', 'counter': 6, 'group_counter': 157, 'group_order': 1296, 'label': '3C', 'order': 3, 'powers': [6, 1], 'representative': 436, 'size': 18}
id: 114460766
{'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 7, 'group_counter': 157, 'group_order': 1296, 'label': '4A', 'order': 4, 'powers': [2, 7], 'representative': 324, 'size': 2}
id: 114460767
{'aut_label': '4B', 'centralizer': '108.g1.a1', 'counter': 8, 'group_counter': 157, 'group_order': 1296, 'label': '4B', 'order': 4, 'powers': [2, 8], 'representative': 407, 'size': 108}
id: 114460768
{'aut_label': '6A', 'centralizer': '2.c1.a1', 'counter': 9, 'group_counter': 157, 'group_order': 1296, 'label': '6A', 'order': 6, 'powers': [4, 2], 'representative': 684, 'size': 2}
id: 114460717
{'aut_label': '6B', 'centralizer': '6.e1.a1', 'counter': 10, 'group_counter': 157, 'group_order': 1296, 'label': '6B', 'order': 6, 'powers': [5, 2], 'representative': 216, 'size': 6}
id: 114460718
{'aut_label': '6C', 'centralizer': '18.a1.a1', 'counter': 11, 'group_counter': 157, 'group_order': 1296, 'label': '6C', 'order': 6, 'powers': [6, 2], 'representative': 260, 'size': 18}
id: 114460719
{'aut_label': '6D1', 'centralizer': '108.b1.a1', 'counter': 12, 'group_counter': 157, 'group_order': 1296, 'label': '6D1', 'order': 6, 'powers': [6, 3], 'representative': 154, 'size': 108}
id: 114460720
{'aut_label': '6D1', 'centralizer': '108.b1.a1', 'counter': 13, 'group_counter': 157, 'group_order': 1296, 'label': '6D-1', 'order': 6, 'powers': [6, 3], 'representative': 110, 'size': 108}
id: 114460721
{'aut_label': '8A1', 'centralizer': '18.j1.a1', 'counter': 14, 'group_counter': 157, 'group_order': 1296, 'label': '8A1', 'order': 8, 'powers': [7, 14], 'representative': 1, 'size': 18}
id: 114460722
{'aut_label': '8A1', 'centralizer': '18.j1.a1', 'counter': 15, 'group_counter': 157, 'group_order': 1296, 'label': '8A-1', 'order': 8, 'powers': [7, 15], 'representative': 973, 'size': 18}
id: 114460723
{'aut_label': '9A1', 'centralizer': '6.g1.a1', 'counter': 16, 'group_counter': 157, 'group_order': 1296, 'label': '9A1', 'order': 9, 'powers': [17, 4], 'representative': 96, 'size': 6}
id: 114460724
{'aut_label': '9A1', 'centralizer': '6.g1.a1', 'counter': 17, 'group_counter': 157, 'group_order': 1296, 'label': '9A2', 'order': 9, 'powers': [18, 4], 'representative': 84, 'size': 6}
id: 114460725
{'aut_label': '9A1', 'centralizer': '6.g1.a1', 'counter': 18, 'group_counter': 157, 'group_order': 1296, 'label': '9A4', 'order': 9, 'powers': [16, 4], 'representative': 60, 'size': 6}
id: 114460726
{'aut_label': '9B', 'centralizer': '36.i1.a1', 'counter': 19, 'group_counter': 157, 'group_order': 1296, 'label': '9B', 'order': 9, 'powers': [19, 4], 'representative': 520, 'size': 36}
id: 114460728
{'aut_label': '12A1', 'centralizer': '2.c1.a1', 'counter': 20, 'group_counter': 157, 'group_order': 1296, 'label': '12A1', 'order': 12, 'powers': [9, 7], 'representative': 396, 'size': 2}
id: 114460729
{'aut_label': '12A1', 'centralizer': '2.c1.a1', 'counter': 21, 'group_counter': 157, 'group_order': 1296, 'label': '12A5', 'order': 12, 'powers': [9, 7], 'representative': 360, 'size': 2}
id: 114460730
{'aut_label': '12B', 'centralizer': '12.b1.a1', 'counter': 22, 'group_counter': 157, 'group_order': 1296, 'label': '12B', 'order': 12, 'powers': [10, 7], 'representative': 108, 'size': 12}
id: 114460731
{'aut_label': '12C', 'centralizer': '36.f1.a1', 'counter': 23, 'group_counter': 157, 'group_order': 1296, 'label': '12C', 'order': 12, 'powers': [11, 7], 'representative': 112, 'size': 36}
id: 114460732
{'aut_label': '12D1', 'centralizer': '108.g1.a1', 'counter': 24, 'group_counter': 157, 'group_order': 1296, 'label': '12D1', 'order': 12, 'powers': [10, 8], 'representative': 119, 'size': 108}
id: 114460733
{'aut_label': '12D1', 'centralizer': '108.g1.a1', 'counter': 25, 'group_counter': 157, 'group_order': 1296, 'label': '12D-1', 'order': 12, 'powers': [10, 8], 'representative': 1235, 'size': 108}
id: 114460734
{'aut_label': '18A1', 'centralizer': '6.g1.a1', 'counter': 26, 'group_counter': 157, 'group_order': 1296, 'label': '18A1', 'order': 18, 'powers': [16, 9], 'representative': 696, 'size': 6}
id: 114460735
{'aut_label': '18A1', 'centralizer': '6.g1.a1', 'counter': 27, 'group_counter': 157, 'group_order': 1296, 'label': '18A5', 'order': 18, 'powers': [18, 9], 'representative': 672, 'size': 6}
id: 114460736
{'aut_label': '18A1', 'centralizer': '6.g1.a1', 'counter': 28, 'group_counter': 157, 'group_order': 1296, 'label': '18A7', 'order': 18, 'powers': [17, 9], 'representative': 660, 'size': 6}
id: 114460737
{'aut_label': '18B', 'centralizer': '36.i1.a1', 'counter': 29, 'group_counter': 157, 'group_order': 1296, 'label': '18B', 'order': 18, 'powers': [19, 9], 'representative': 752, 'size': 36}
id: 114460739
{'aut_label': '24A1', 'centralizer': '18.j1.a1', 'counter': 30, 'group_counter': 157, 'group_order': 1296, 'label': '24A1', 'order': 24, 'powers': [21, 14], 'representative': 361, 'size': 18}
id: 114460740
{'aut_label': '24A1', 'centralizer': '18.j1.a1', 'counter': 31, 'group_counter': 157, 'group_order': 1296, 'label': '24A-1', 'order': 24, 'powers': [21, 15], 'representative': 721, 'size': 18}
id: 114460741
{'aut_label': '24A1', 'centralizer': '18.j1.a1', 'counter': 32, 'group_counter': 157, 'group_order': 1296, 'label': '24A5', 'order': 24, 'powers': [20, 15], 'representative': 1045, 'size': 18}
id: 114460742
{'aut_label': '24A1', 'centralizer': '18.j1.a1', 'counter': 33, 'group_counter': 157, 'group_order': 1296, 'label': '24A-5', 'order': 24, 'powers': [20, 14], 'representative': 37, 'size': 18}
id: 114460743
{'aut_label': '36A1', 'centralizer': '6.g1.a1', 'counter': 34, 'group_counter': 157, 'group_order': 1296, 'label': '36A1', 'order': 36, 'powers': [26, 21], 'representative': 348, 'size': 6}
id: 114460744
{'aut_label': '36A1', 'centralizer': '6.g1.a1', 'counter': 35, 'group_counter': 157, 'group_order': 1296, 'label': '36A5', 'order': 36, 'powers': [27, 20], 'representative': 336, 'size': 6}
id: 114460745
{'aut_label': '36A1', 'centralizer': '6.g1.a1', 'counter': 36, 'group_counter': 157, 'group_order': 1296, 'label': '36A7', 'order': 36, 'powers': [28, 20], 'representative': 1032, 'size': 6}
id: 114460746
{'aut_label': '36A1', 'centralizer': '6.g1.a1', 'counter': 37, 'group_counter': 157, 'group_order': 1296, 'label': '36A11', 'order': 36, 'powers': [28, 21], 'representative': 1020, 'size': 6}
id: 114460747
{'aut_label': '36A1', 'centralizer': '6.g1.a1', 'counter': 38, 'group_counter': 157, 'group_order': 1296, 'label': '36A13', 'order': 36, 'powers': [27, 21], 'representative': 420, 'size': 6}
id: 114460748
{'aut_label': '36A1', 'centralizer': '6.g1.a1', 'counter': 39, 'group_counter': 157, 'group_order': 1296, 'label': '36A17', 'order': 36, 'powers': [26, 20], 'representative': 408, 'size': 6}
id: 114460750
{'aut_label': '36B1', 'centralizer': '36.i1.a1', 'counter': 40, 'group_counter': 157, 'group_order': 1296, 'label': '36B1', 'order': 36, 'powers': [29, 20], 'representative': 124, 'size': 36}
id: 114460751
{'aut_label': '36B1', 'centralizer': '36.i1.a1', 'counter': 41, 'group_counter': 157, 'group_order': 1296, 'label': '36B5', 'order': 36, 'powers': [29, 21], 'representative': 136, 'size': 36}
id: 114460752
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 42, 'group_counter': 157, 'group_order': 1296, 'label': '72A1', 'order': 72, 'powers': [34, 30], 'representative': 13, 'size': 18}
id: 114460753
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 43, 'group_counter': 157, 'group_order': 1296, 'label': '72A-1', 'order': 72, 'powers': [34, 31], 'representative': 661, 'size': 18}
id: 114460754
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 44, 'group_counter': 157, 'group_order': 1296, 'label': '72A5', 'order': 72, 'powers': [35, 32], 'representative': 121, 'size': 18}
id: 114460755
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 45, 'group_counter': 157, 'group_order': 1296, 'label': '72A-5', 'order': 72, 'powers': [35, 33], 'representative': 457, 'size': 18}
id: 114460756
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 46, 'group_counter': 157, 'group_order': 1296, 'label': '72A7', 'order': 72, 'powers': [36, 32], 'representative': 553, 'size': 18}
id: 114460757
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 47, 'group_counter': 157, 'group_order': 1296, 'label': '72A-7', 'order': 72, 'powers': [36, 33], 'representative': 25, 'size': 18}
id: 114460758
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 48, 'group_counter': 157, 'group_order': 1296, 'label': '72A11', 'order': 72, 'powers': [37, 30], 'representative': 17, 'size': 18}
id: 114460759
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 49, 'group_counter': 157, 'group_order': 1296, 'label': '72A-11', 'order': 72, 'powers': [37, 31], 'representative': 229, 'size': 18}
id: 114460761
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 50, 'group_counter': 157, 'group_order': 1296, 'label': '72A13', 'order': 72, 'powers': [38, 31], 'representative': 133, 'size': 18}
id: 114460762
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 51, 'group_counter': 157, 'group_order': 1296, 'label': '72A-13', 'order': 72, 'powers': [38, 30], 'representative': 445, 'size': 18}
id: 114460763
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 52, 'group_counter': 157, 'group_order': 1296, 'label': '72A17', 'order': 72, 'powers': [39, 33], 'representative': 889, 'size': 18}
id: 114460764
{'aut_label': '72A1', 'centralizer': '18.j1.a1', 'counter': 53, 'group_counter': 157, 'group_order': 1296, 'label': '72A-17', 'order': 72, 'powers': [39, 32], 'representative': 241, 'size': 18}

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: 5345109
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 5345120
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 5345127
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 5345128
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 5345129
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 5345130
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, 2, 0, 2, 2, -1, -1, -1, 0, 0, 2, 2, 2, -1, 2, 2, 2, -1, 0, 0, 2, 2, 2, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345131
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, -2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345132
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -1, 2, 0, 2, 2, -1, 1, 1, 0, 0, 2, 2, 2, -1, 2, 2, 2, -1, 0, 0, 2, 2, 2, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345133
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, -2, -2, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 5345110
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2f', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, 0, 4, 4, 4, 0, 0, -4, -4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345111
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2g', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 4, -4, 0, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, -4, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345112
{'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2h', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, -2, -4, 0, 4, 4, -2, 0, 0, 0, 0, 4, 4, 4, -2, -4, -4, -4, 2, 0, 0, 4, 4, 4, -2, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345114
{'cdim': 4, 'counter': 14, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, -2, 4, 0, 4, 4, -2, 0, 0, 0, 0, -2, -2, -2, 1, 4, 4, 4, -2, 0, 0, -2, -2, -2, 1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345115
{'cdim': 4, 'counter': 15, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.4b', 'multiplicity': 1, 'nt': [12, 38], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, -2, -4, 0, 4, 4, -2, 0, 0, 0, 0, -2, -2, -2, 1, -4, -4, -4, 2, 0, 0, -2, -2, -2, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345116
{'cdim': 4, 'counter': 16, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.4c', 'multiplicity': 1, 'nt': [24, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 4, 4, -2, 0, 0, -4, -4, 2, 0, 0, 0, 0, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 5345118
{'cdim': 6, 'counter': 18, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.6a', 'multiplicity': 1, 'nt': [9, 18], 'qdim': 6, 'qvalues': [6, 6, 0, 6, -3, 0, 6, 2, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345119
{'cdim': 6, 'counter': 19, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.6b', 'multiplicity': 1, 'nt': [18, 51], 'qdim': 6, 'qvalues': [6, 6, 0, 6, -3, 0, 6, -2, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345113
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.2i', 'multiplicity': 4, 'nt': [24, 35], 'qdim': 8, 'qvalues': [8, -8, 0, 8, 8, 8, 0, 0, -8, -8, -8, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345117
{'cdim': 4, 'counter': 17, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.4d', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 8, 8, -4, 0, 0, -8, -8, 4, 0, 0, 0, 0, -4, -4, -4, 2, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 5345121
{'cdim': 6, 'counter': 20, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.6c', 'multiplicity': 2, 'nt': [36, 231], 'qdim': 12, 'qvalues': [12, 12, 0, 12, -6, 0, -12, 0, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345126
{'cdim': 12, 'counter': 25, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.12a', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -12, 0, 12, -6, 0, 0, 0, -12, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345122
{'cdim': 6, 'counter': 21, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.6d', 'multiplicity': 3, 'nt': [27, 124], 'qdim': 18, 'qvalues': [18, 18, 0, -9, 0, 0, 18, 0, -9, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345123
{'cdim': 6, 'counter': 22, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.6e', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, 0, -9, 0, 0, 18, 0, -9, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345124
{'cdim': 6, 'counter': 23, 'faithful': False, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.6f', 'multiplicity': 6, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, 36, 0, -18, 0, 0, -36, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5345125
{'cdim': 6, 'counter': 24, 'faithful': True, 'group': '1296.157', 'group_order': 1296, 'image': None, 'label': '1296.157.6g', 'multiplicity': 12, 'nt': [216, 0], 'qdim': 72, 'qvalues': [72, -72, 0, -36, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 10401110
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1296, 'label': '1296.157.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10401121
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 648, 'label': '1296.157.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10401132
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 648, 'label': '1296.157.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 10401143
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 648, 'label': '1296.157.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 10401154
{'center': '6.b1.a1', 'center_index': 6, 'center_order': 216, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 216, 'label': '1296.157.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10401159
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 216, 'label': '1296.157.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401160
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 324, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 162, 'label': '1296.157.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401161
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 108, 'label': '1296.157.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401162
{'center': '6.b1.a1', 'center_index': 6, 'center_order': 216, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 108, 'label': '1296.157.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 10401111
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 162, 'counter': 10, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 81, 'label': '1296.157.2f1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
id: 10401112
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 162, 'counter': 11, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 81, 'label': '1296.157.2f2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
id: 10401113
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 12, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 54, 'label': '1296.157.2g1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
id: 10401114
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 13, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 54, 'label': '1296.157.2g2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
id: 10401115
{'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 14, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 54, 'label': '1296.157.2h1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401116
{'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 54, 'label': '1296.157.2h2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401117
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 16, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 27, 'label': '1296.157.2i1', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]]]}
id: 10401118
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 17, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 27, 'label': '1296.157.2i2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]]]}
id: 10401119
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 18, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 27, 'label': '1296.157.2i3', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]]]}
id: 10401120
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 19, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 27, 'label': '1296.157.2i4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]]]}
id: 10401122
{'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 20, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 36, 'label': '1296.157.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401123
{'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '72.23', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 18, 'label': '1296.157.4b', 'nt': [12, 38], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401124
{'center': '24.b1.a1', 'center_index': 24, 'center_order': 54, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '48.16', 'image_order': 48, 'indicator': -1, 'kernel': '48.b1.a1', 'kernel_order': 27, 'label': '1296.157.4c', 'nt': [24, 42], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401125
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 18, 'counter': 23, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '144.59', 'image_order': 144, 'indicator': -1, 'kernel': '144.a1.a1', 'kernel_order': 9, 'label': '1296.157.4d1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401126
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 18, 'counter': 24, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '144.59', 'image_order': 144, 'indicator': -1, 'kernel': '144.a1.a1', 'kernel_order': 9, 'label': '1296.157.4d2', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401127
{'center': '108.a1.a1', 'center_index': 108, 'center_order': 12, 'counter': 25, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 12, 'label': '1296.157.6a', 'nt': [9, 18], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401128
{'center': '108.a1.a1', 'center_index': 108, 'center_order': 12, 'counter': 26, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 12, 'label': '1296.157.6b', 'nt': [18, 51], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401129
{'center': '108.a1.a1', 'center_index': 108, 'center_order': 12, 'counter': 27, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '216.37', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 6, 'label': '1296.157.6c1', 'nt': [36, 231], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401130
{'center': '108.a1.a1', 'center_index': 108, 'center_order': 12, 'counter': 28, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '216.37', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 6, 'label': '1296.157.6c2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10401131
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 29, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '324.40', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 4, 'label': '1296.157.6d1', 'nt': [27, 124], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]]]}
id: 10401133
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 30, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '324.40', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 4, 'label': '1296.157.6d2', 'nt': [27, 124], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
id: 10401134
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 31, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '324.40', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 4, 'label': '1296.157.6d3', 'nt': [27, 124], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]]]}
id: 10401135
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 32, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '324.40', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 4, 'label': '1296.157.6e1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]]]}
id: 10401136
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 33, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '324.40', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 4, 'label': '1296.157.6e2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
id: 10401137
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 34, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '324.40', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 4, 'label': '1296.157.6e3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]]]}
id: 10401138
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 35, 'cyclotomic_n': 36, 'dim': 6, 'faithful': False, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '648.77', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 2, 'label': '1296.157.6f1', 'nt': [108, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[0, 0]], [[0, 0]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]]]}
id: 10401139
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 36, 'cyclotomic_n': 36, 'dim': 6, 'faithful': False, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '648.77', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 2, 'label': '1296.157.6f2', 'nt': [108, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[0, 0]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[0, 0]], [[0, 0]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]]]}
id: 10401140
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 37, 'cyclotomic_n': 36, 'dim': 6, 'faithful': False, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '648.77', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 2, 'label': '1296.157.6f3', 'nt': [108, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]]]}
id: 10401141
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 38, 'cyclotomic_n': 36, 'dim': 6, 'faithful': False, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '648.77', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 2, 'label': '1296.157.6f4', 'nt': [108, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[0, 0]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 5], [1, -5]]]}
id: 10401142
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 39, 'cyclotomic_n': 36, 'dim': 6, 'faithful': False, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '648.77', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 2, 'label': '1296.157.6f5', 'nt': [108, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]], [[1, 1], [1, -1]]]}
id: 10401144
{'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 36, 'dim': 6, 'faithful': False, 'field': [-3, 0, 9, 0, -6, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '648.77', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 2, 'label': '1296.157.6f6', 'nt': [108, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 4], [-2, 8], [1, 10]], [[-2, 2], [-2, 4], [1, 8], [1, 10]], [[1, 2], [1, 4], [1, 8], [-2, 10]], [[0, 0]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[2, 2], [2, 4], [-1, 8], [-1, 10]], [[-1, 2], [-1, 4], [-1, 8], [2, 10]], [[-1, 2], [-1, 4], [2, 8], [-1, 10]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]]]}
id: 10401145
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g1', 'nt': [216, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 9], [-1, 15]], [[-1, 3], [1, 9], [1, 15]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[0, 0]], [[-3, 6], [-3, -6]], [[3, 6], [3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[0, 0]], [[1, 15], [1, 21]], [[-1, 15], [-1, 21]], [[1, 3], [-1, 9], [1, 21]], [[-1, 3], [1, 9], [-1, 21]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[0, 0]], [[0, 0]], [[-1, 5], [1, 7], [-1, 19]], [[1, 1], [-1, 11], [-1, 13]], [[1, 5], [-1, 7], [1, 19]], [[1, 17], [1, 19]], [[-1, 1], [1, 11], [-1, 23]], [[1, 5], [-1, 7], [-1, 17]], [[1, 13], [1, 23]], [[-1, 5], [1, 7], [1, 17]], [[1, 1], [-1, 11], [1, 23]], [[-1, 1], [1, 11], [1, 13]], [[-1, 17], [-1, 19]], [[-1, 13], [-1, 23]]]}
id: 10401155
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 50, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g10', 'nt': [216, 12], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 9], [1, 15]], [[1, 3], [-1, 9], [-1, 15]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[0, 0]], [[-3, 6], [-3, -6]], [[3, 6], [3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[0, 0]], [[-1, 15], [-1, 21]], [[1, 15], [1, 21]], [[-1, 3], [1, 9], [-1, 21]], [[1, 3], [-1, 9], [1, 21]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[0, 0]], [[0, 0]], [[-1, 5], [1, 7], [1, 17]], [[1, 1], [-1, 11], [1, 23]], [[1, 5], [-1, 7], [-1, 17]], [[1, 5], [-1, 7], [1, 19]], [[-1, 13], [-1, 23]], [[-1, 17], [-1, 19]], [[-1, 1], [1, 11], [1, 13]], [[1, 17], [1, 19]], [[1, 13], [1, 23]], [[-1, 1], [1, 11], [-1, 23]], [[-1, 5], [1, 7], [-1, 19]], [[1, 1], [-1, 11], [-1, 13]]]}
id: 10401156
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id: 10401157
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 52, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g12', 'nt': [216, 12], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 9], [1, 15]], [[1, 3], [-1, 9], [-1, 15]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[0, 0]], [[3, 6], [3, -6]], [[-3, 6], [-3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[0, 0]], [[1, 3], [-1, 9], [1, 21]], [[-1, 3], [1, 9], [-1, 21]], [[1, 15], [1, 21]], [[-1, 15], [-1, 21]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 11], [-1, 13]], [[1, 17], [1, 19]], [[-1, 1], [1, 11], [1, 13]], [[1, 13], [1, 23]], [[-1, 5], [1, 7], [-1, 19]], [[-1, 1], [1, 11], [-1, 23]], [[1, 5], [-1, 7], [-1, 17]], [[1, 1], [-1, 11], [1, 23]], [[1, 5], [-1, 7], [1, 19]], [[-1, 17], [-1, 19]], [[-1, 13], [-1, 23]], [[-1, 5], [1, 7], [1, 17]]]}
id: 10401146
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 42, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g2', 'nt': [216, 12], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 9], [1, 15]], [[1, 3], [-1, 9], [-1, 15]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[0, 0]], [[-3, 6], [-3, -6]], [[3, 6], [3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[0, 0]], [[-1, 15], [-1, 21]], [[1, 15], [1, 21]], [[-1, 3], [1, 9], [-1, 21]], [[1, 3], [-1, 9], [1, 21]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[0, 0]], [[0, 0]], [[1, 5], [-1, 7], [1, 19]], [[-1, 1], [1, 11], [1, 13]], [[-1, 5], [1, 7], [-1, 19]], [[-1, 17], [-1, 19]], [[1, 1], [-1, 11], [1, 23]], [[-1, 5], [1, 7], [1, 17]], [[-1, 13], [-1, 23]], [[1, 5], [-1, 7], [-1, 17]], [[-1, 1], [1, 11], [-1, 23]], [[1, 1], [-1, 11], [-1, 13]], [[1, 17], [1, 19]], [[1, 13], [1, 23]]]}
id: 10401147
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 43, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g3', 'nt': [216, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 9], [-1, 15]], [[-1, 3], [1, 9], [1, 15]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[0, 0]], [[3, 6], [3, -6]], [[-3, 6], [-3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[0, 0]], [[-1, 3], [1, 9], [-1, 21]], [[1, 3], [-1, 9], [1, 21]], [[-1, 15], [-1, 21]], [[1, 15], [1, 21]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[0, 0]], [[0, 0]], [[-1, 13], [-1, 23]], [[-1, 5], [1, 7], [1, 17]], [[1, 13], [1, 23]], [[1, 1], [-1, 11], [1, 23]], [[-1, 17], [-1, 19]], [[-1, 1], [1, 11], [1, 13]], [[1, 5], [-1, 7], [1, 19]], [[1, 1], [-1, 11], [-1, 13]], [[1, 17], [1, 19]], [[1, 5], [-1, 7], [-1, 17]], [[-1, 1], [1, 11], [-1, 23]], [[-1, 5], [1, 7], [-1, 19]]]}
id: 10401148
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 44, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g4', 'nt': [216, 12], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 9], [1, 15]], [[1, 3], [-1, 9], [-1, 15]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[0, 0]], [[3, 6], [3, -6]], [[-3, 6], [-3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[0, 0]], [[1, 3], [-1, 9], [1, 21]], [[-1, 3], [1, 9], [-1, 21]], [[1, 15], [1, 21]], [[-1, 15], [-1, 21]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[0, 0]], [[0, 0]], [[1, 13], [1, 23]], [[1, 5], [-1, 7], [-1, 17]], [[-1, 13], [-1, 23]], [[-1, 1], [1, 11], [-1, 23]], [[1, 17], [1, 19]], [[1, 1], [-1, 11], [-1, 13]], [[-1, 5], [1, 7], [-1, 19]], [[-1, 1], [1, 11], [1, 13]], [[-1, 17], [-1, 19]], [[-1, 5], [1, 7], [1, 17]], [[1, 1], [-1, 11], [1, 23]], [[1, 5], [-1, 7], [1, 19]]]}
id: 10401149
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id: 10401150
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 46, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g6', 'nt': [216, 12], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 9], [1, 15]], [[1, 3], [-1, 9], [-1, 15]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[0, 0]], [[-3, 6], [-3, -6]], [[3, 6], [3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[0, 0]], [[-1, 15], [-1, 21]], [[1, 15], [1, 21]], [[-1, 3], [1, 9], [-1, 21]], [[1, 3], [-1, 9], [1, 21]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[0, 0]], [[0, 0]], [[-1, 17], [-1, 19]], [[-1, 13], [-1, 23]], [[1, 17], [1, 19]], [[-1, 5], [1, 7], [1, 17]], [[-1, 1], [1, 11], [1, 13]], [[1, 5], [-1, 7], [1, 19]], [[1, 1], [-1, 11], [1, 23]], [[-1, 5], [1, 7], [-1, 19]], [[1, 1], [-1, 11], [-1, 13]], [[1, 13], [1, 23]], [[1, 5], [-1, 7], [-1, 17]], [[-1, 1], [1, 11], [-1, 23]]]}
id: 10401151
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 47, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g7', 'nt': [216, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 9], [-1, 15]], [[-1, 3], [1, 9], [1, 15]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[0, 0]], [[3, 6], [3, -6]], [[-3, 6], [-3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[0, 0]], [[-1, 3], [1, 9], [-1, 21]], [[1, 3], [-1, 9], [1, 21]], [[-1, 15], [-1, 21]], [[1, 15], [1, 21]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 11], [1, 23]], [[1, 5], [-1, 7], [1, 19]], [[-1, 1], [1, 11], [-1, 23]], [[-1, 1], [1, 11], [1, 13]], [[-1, 5], [1, 7], [1, 17]], [[-1, 13], [-1, 23]], [[-1, 17], [-1, 19]], [[1, 13], [1, 23]], [[1, 5], [-1, 7], [-1, 17]], [[-1, 5], [1, 7], [-1, 19]], [[1, 1], [-1, 11], [-1, 13]], [[1, 17], [1, 19]]]}
id: 10401152
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 48, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g8', 'nt': [216, 12], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 9], [1, 15]], [[1, 3], [-1, 9], [-1, 15]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[0, 0]], [[3, 6], [3, -6]], [[-3, 6], [-3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[0, 0]], [[1, 3], [-1, 9], [1, 21]], [[-1, 3], [1, 9], [-1, 21]], [[1, 15], [1, 21]], [[-1, 15], [-1, 21]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 11], [-1, 23]], [[-1, 5], [1, 7], [-1, 19]], [[1, 1], [-1, 11], [1, 23]], [[1, 1], [-1, 11], [-1, 13]], [[1, 5], [-1, 7], [-1, 17]], [[1, 13], [1, 23]], [[1, 17], [1, 19]], [[-1, 13], [-1, 23]], [[-1, 5], [1, 7], [1, 17]], [[1, 5], [-1, 7], [1, 19]], [[-1, 1], [1, 11], [1, 13]], [[-1, 17], [-1, 19]]]}
id: 10401153
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 2, 'counter': 49, 'cyclotomic_n': 72, 'dim': 6, 'faithful': True, 'field': [1, 0, 36, 0, 105, 0, 112, 0, 54, 0, 12, 0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.157', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.157.6g9', 'nt': [216, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 9], [-1, 15]], [[-1, 3], [1, 9], [1, 15]], [[1, 4], [1, 8], [1, 16], [-2, 20]], [[-2, 4], [-2, 8], [1, 16], [1, 20]], [[1, 4], [1, 8], [-2, 16], [1, 20]], [[0, 0]], [[-3, 6], [-3, -6]], [[3, 6], [3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, 8], [2, 16], [-1, 20]], [[2, 4], [2, 8], [-1, 16], [-1, 20]], [[-1, 4], [-1, 8], [-1, 16], [2, 20]], [[0, 0]], [[1, 15], [1, 21]], [[-1, 15], [-1, 21]], [[1, 3], [-1, 9], [1, 21]], [[-1, 3], [1, 9], [-1, 21]], [[1, 2], [1, 10], [1, 14], [-2, 22]], [[-1, 2], [-1, 10], [2, 14], [-1, 22]], [[2, 2], [2, 10], [-1, 14], [-1, 22]], [[1, 2], [1, 10], [-2, 14], [1, 22]], [[-1, 2], [-1, 10], [-1, 14], [2, 22]], [[-2, 2], [-2, 10], [1, 14], [1, 22]], [[0, 0]], [[0, 0]], [[1, 5], [-1, 7], [-1, 17]], [[-1, 1], [1, 11], [-1, 23]], [[-1, 5], [1, 7], [1, 17]], [[-1, 5], [1, 7], [-1, 19]], [[1, 13], [1, 23]], [[1, 17], [1, 19]], [[1, 1], [-1, 11], [-1, 13]], [[-1, 17], [-1, 19]], [[-1, 13], [-1, 23]], [[1, 1], [-1, 11], [1, 23]], [[1, 5], [-1, 7], [1, 19]], [[-1, 1], [1, 11], [1, 13]]]}
id: 10401158
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 53, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1296.157', 'group_counter': 157, 'group_order': 1296, 'image': None, 'image_isoclass': '432.85', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 3, 'label': '1296.157.12a', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema
Showing the first 100 of 112 matching records in this table.

id: 70719341
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1296, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1296.157.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '1296.157', 'subgroup_hash': 157, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times C_{36}).D_6', 'supersolvable': True, 'sylow': 0}
id: 70719365
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.2.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': '648.137', 'subgroup_hash': 137, 'subgroup_order': 648, 'subgroup_tex': '\\He_3.D_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719376
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.182', 'subgroup_hash': 182, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_{36}).S_3', 'supersolvable': True, 'sylow': 0}
id: 70719387
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 648, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.21', 'subgroup_hash': 21, 'subgroup_order': 648, 'subgroup_tex': '\\He_3.C_{24}', 'supersolvable': True, 'sylow': 0}
id: 70719398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 216, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.78', 'subgroup_hash': 78, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
id: 70719409
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 216, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.63', 'subgroup_hash': 63, 'subgroup_order': 432, 'subgroup_tex': 'C_6.D_{36}', 'supersolvable': True, 'sylow': 0}
id: 70719420
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 324, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.32', 'subgroup_hash': 32, 'subgroup_order': 324, 'subgroup_tex': 'C_{12}.\\He_3', 'supersolvable': True, 'sylow': 0}
id: 70719431
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.71', 'subgroup_hash': 71, 'subgroup_order': 324, 'subgroup_tex': '\\He_3.D_6', 'supersolvable': True, 'sylow': 0}
id: 70719442
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.23', 'subgroup_hash': 23, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times C_{18}).S_3', 'supersolvable': True, 'sylow': 0}
id: 70719342
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 216, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.65', 'subgroup_hash': 65, 'subgroup_order': 216, 'subgroup_tex': 'C_3:D_{36}', 'supersolvable': True, 'sylow': 0}
id: 70719353
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 216, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.17', 'subgroup_hash': 17, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 70719357
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.51', 'subgroup_hash': 51, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719358
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.49', 'subgroup_hash': 49, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719359
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.43', 'subgroup_hash': 43, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}.C_6', 'supersolvable': True, 'sylow': 0}
id: 70719360
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.52', 'subgroup_hash': 52, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}.C_6', 'supersolvable': True, 'sylow': 0}
id: 70719361
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.13', 'subgroup_hash': 13, 'subgroup_order': 216, 'subgroup_tex': 'C_3:C_{72}', 'supersolvable': True, 'sylow': 0}
id: 70719362
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 162, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.29', 'subgroup_hash': 29, 'subgroup_order': 162, 'subgroup_tex': 'C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
id: 70719363
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.13', 'subgroup_hash': 13, 'subgroup_order': 162, 'subgroup_tex': '\\He_3.S_3', 'supersolvable': True, 'sylow': 0}
id: 70719364
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.9.a1.a1', 'maximal': False, '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': '144.59', 'subgroup_hash': 59, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719366
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '144.60', 'subgroup_hash': 60, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719367
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '144.7', 'subgroup_hash': 7, 'subgroup_order': 144, 'subgroup_tex': 'C_{72}:C_2', 'supersolvable': True, 'sylow': 0}
id: 70719368
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 108, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.13', 'subgroup_hash': 13, 'subgroup_order': 108, 'subgroup_tex': 'C_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 70719369
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.12', 'subgroup_hash': 12, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
id: 70719370
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.12.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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
id: 70719371
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 70719372
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719374
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719375
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719377
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.12.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a2', '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': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 81, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1296.157.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.8', 'subgroup_hash': 8, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 3}
id: 70719379
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.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': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719380
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.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': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719381
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.6', 'subgroup_hash': 6, 'subgroup_order': 72, 'subgroup_tex': 'D_{36}', 'supersolvable': True, 'sylow': 0}
id: 70719382
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719383
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
id: 70719384
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719385
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
id: 70719386
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.4', 'subgroup_hash': 4, 'subgroup_order': 72, 'subgroup_tex': 'C_9:Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719388
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.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': '72.4', 'subgroup_hash': 4, 'subgroup_order': 72, 'subgroup_tex': 'C_9:Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719389
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.j1.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': '72.2', 'subgroup_hash': 2, 'subgroup_order': 72, 'subgroup_tex': 'C_{72}', 'supersolvable': True, 'sylow': 0}
id: 70719390
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 54, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 70719391
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 54, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 70719392
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
id: 70719393
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 70719394
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
id: 70719395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 70719396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
id: 70719397
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.27.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
id: 70719399
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.36.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': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719400
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 70719401
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
id: 70719402
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
id: 70719403
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719404
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719405
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 70719406
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
id: 70719407
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.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': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
id: 70719408
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.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': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
id: 70719410
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.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': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
id: 70719411
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.36.k1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a2', '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': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
id: 70719412
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 27, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:C_2', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 70719413
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 27, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.16', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 70719414
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
id: 70719415
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 70719416
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719417
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719418
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719419
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
id: 70719421
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719422
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 70719423
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719424
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1.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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 70719425
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 18, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.23', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 70719426
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.72.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 70719427
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 70719428
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 70719429
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 70719430
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 70719432
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
id: 70719433
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1296.157.81.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 2}
id: 70719434
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 12, 'counter': 82, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.157.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719435
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 70719436
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 70719437
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 70719438
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 70719439
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719440
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719441
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 70719443
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1.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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 70719444
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 9, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.157.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.59', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 59, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.D_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], '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: 70719445
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 70719446
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 93, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 70719447
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': 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: 70719448
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.162.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 70719449
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.157.162.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 70719450
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 70719451
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 6, 'counter': 98, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.157.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_{12}', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 70719452
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': 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: 70719343
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.157', 'ambient_counter': 157, 'ambient_order': 1296, 'ambient_tex': '(C_3\\times C_{36}).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.157.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': 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}

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

gps_subgroup_data • Show schema
Showing the first 100 of 112 matching records in this table.

id: 70719341
{'ambient': '1296.157', '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': '648.a1.a1', 'complements': ['1296.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '3.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6288, 5842, 6303, 5727, 6249, 5593, 6363, 5588], 'generators': [1, 4, 84, 6, 648, 36, 468, 324], 'label': '1296.157.1.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.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '648.77', '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': '648.77'}
id: 70719342
{'ambient': '1296.157', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '648.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '18.b1.a1', '18.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4067, 8954, 5737, 2969, 4772, 2713, 4269, 8514], 'generators': [6, 36, 468, 324, 648, 84], 'label': '1296.157.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '648.77', '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': '648.77'}
id: 70719343
{'ambient': '1296.157', 'aut_centralizer_order': 864, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 7776, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '108.b1.a1', '108.h1.a1', '108.i1.a1'], 'contains': ['432.c1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4655, -1, 4960, -1, 5166, -1, 5604, -1], 'generators': [648, 4], 'label': '1296.157.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719344
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 7776, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '108.b1.a1'], 'contains': ['432.c1.a1', '648.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2887, -1, 3215, -1, 4223, -1, 4075, -1], 'generators': [6, 4], 'label': '1296.157.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '216.d1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 70719345
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2592, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.f1.a1', '72.g1.a1', '108.c1.a1'], 'contains': ['432.a1.a1', '648.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1375, -1, 1748, -1, 3161, -1, 3155, -1], 'generators': [6, 36], 'label': '1296.157.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '216.e1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 70719346
{'ambient': '1296.157', 'aut_centralizer_order': 24, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2592, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '108.d1.a1'], 'contains': ['432.b1.a1', '648.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1982, -1, 2198, -1, 3786, -1, 3411, -1], 'generators': [6, 468], 'label': '1296.157.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1.a1', 'old_label': '216.f1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 70719347
{'ambient': '1296.157', 'aut_centralizer_order': 7776, 'aut_label': '324.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 7776, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.f1.a1', '108.h1.a1', '162.a1.a1', '162.b1.a1', '162.c1.a1'], 'contains': ['648.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7094, 6878, 7379, 7087, 7380, 7454, 6951, 7846], 'generators': [324], 'label': '1296.157.324.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': ['108.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '648.77', 'quotient_action_image': '2.1', 'quotient_action_kernel': '162.12', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719348
{'ambient': '1296.157', 'aut_centralizer_order': 144, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 7776, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.c1.a1', '108.d1.a1', '162.a1.a1'], 'contains': ['648.a1.a1', '648.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3718, -1, 4431, -1, 4869, -1, 4525, -1], 'generators': [6, 648], 'label': '1296.157.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '648.77', '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': '2.1'}
id: 70719349
{'ambient': '1296.157', 'aut_centralizer_order': 144, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 7776, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '108.g1.a1', '108.i1.a1', '162.b1.a1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5076, -1, 6296, -1, 5569, -1, 5204, -1], 'generators': [7], 'label': '1296.157.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1.a1', 'old_label': '324.c1.a1', 'projective_image': '648.77', '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': '2.1'}
id: 70719350
{'ambient': '1296.157', 'aut_centralizer_order': 7776, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 7776, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '216.a1.a1', '216.e1.a1'], 'contains': ['1296.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1375, 4911, 1660, 5065, 3161, 5418, 3155, 5811], 'generators': [36], 'label': '1296.157.432.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['144.a1.a1', '216.a1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '1296.157', 'quotient_action_image': '2.1', 'quotient_action_kernel': '216.14', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719351
{'ambient': '1296.157', 'aut_centralizer_order': 2592, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 7776, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '216.b1.a1', '216.f1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1877, -1, 2050, -1, 3786, -1, 3440, -1], 'generators': [468], 'label': '1296.157.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '432.b1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719352
{'ambient': '1296.157', 'aut_centralizer_order': 864, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 7776, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '216.c1.a1', '216.d1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2758, -1, 3184, -1, 4223, -1, 4016, -1], 'generators': [4], 'label': '1296.157.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '432.c1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719353
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.545', 'aut_weyl_index': 36, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.e1.a1', '18.g1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8721, 3175, 8766, 8943, 7701, 8616, 8159, 2568], 'generators': [1, 36, 504, 324, 648, 4], 'label': '1296.157.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
id: 70719354
{'ambient': '1296.157', 'aut_centralizer_order': 15552, 'aut_label': '648.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 15552, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '324.a1.a1', '324.b1.a1', '324.c1.a1'], 'contains': ['1296.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3718, 5895, 4431, 6075, 4869, 6563, 4525, 6956], 'generators': [648], 'label': '1296.157.648.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['216.a1.a1', '324.a1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '648.77', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.77', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 70719355
{'ambient': '1296.157', 'aut_centralizer_order': 144, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 15552, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '216.e1.a1', '216.f1.a1', '324.b1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2180, -1, 2428, -1, 4004, -1, 3772, -1], 'generators': [6], 'label': '1296.157.648.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '648.b1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 70719356
{'ambient': '1296.157', 'aut_centralizer_order': None, 'aut_label': '1296.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': ['432.a1.a1', '432.b1.a1', '432.c1.a1', '648.a1.a1', '648.b1.a1'], 'contains': [], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2180, 5412, 2428, 5580, 4004, 5990, 3772, 6383], 'generators': [], 'label': '1296.157.1296.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': ['432.a1.a1', '648.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1296.a1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 70719357
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.2470', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '18.a1.a1', '18.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6588, -1, 7737, -1, 5767, -1, 5895, -1], 'generators': [6, 36, 468, 324, 4, 648], 'label': '1296.157.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '216.35'}
id: 70719358
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.2470', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '18.d1.a1', '18.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7765, -1, 6474, -1, 6379, -1, 6489, -1], 'generators': [7, 36, 4, 324, 468, 648], 'label': '1296.157.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '216.35'}
id: 70719359
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.2583', 'aut_weyl_index': 18, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.g1.a1', '18.d1.a1', '18.h1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4523, -1, 5199, -1, 5205, -1, 5351, -1], 'generators': [7, 36, 84, 324, 468, 648], 'label': '1296.157.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.e1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.6'}
id: 70719360
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.362', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.f1.a1', '12.h1.a1', '12.h1.a2', '18.d1.a1', '18.i1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5194, -1, 2995, -1, 4320, -1, 3831, -1], 'generators': [7, 36, 496, 324, 468, 648], 'label': '1296.157.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '6.f1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
id: 70719361
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.195', 'aut_weyl_index': 108, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '18.e1.a1', '18.j1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7180, -1, 7161, -1, 6934, -1, 7027, -1], 'generators': [1, 504, 648, 48, 324, 36], 'label': '1296.157.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.g1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719362
{'ambient': '1296.157', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '324.117', 'aut_weyl_index': 48, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1899, 2818, 1660, 2619, 681, 2506, 1108, 2266], 'generators': [648, 36, 4, 48, 468], 'label': '1296.157.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
id: 70719363
{'ambient': '1296.157', 'aut_centralizer_order': 4, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '972.446', 'aut_weyl_index': 16, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '24.d1.a1', '24.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [792, -1, 899, -1, 187, -1, 138, -1], 'generators': [6, 36, 4, 84, 468], 'label': '1296.157.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '162.13'}
id: 70719364
{'ambient': '1296.157', 'aut_centralizer_order': 3, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 27, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.a1.a1', '18.f1.a1', '18.g1.a1', '27.a1.a1', '27.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8903, -1, 8850, -1, 8535, -1, 8580, -1], 'generators': [1, 36, 4, 6, 324, 648], 'label': '1296.157.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '648.77', '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': '72.23'}
id: 70719365
{'ambient': '1296.157', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '648.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '6.a1.a1', '6.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4943, 9258, 5600, 2215, 4626, 2554, 4775, 8625], 'generators': [6, 468, 84, 324, 36, 4, 648], 'label': '1296.157.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '648.77', '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': '648.77'}
id: 70719366
{'ambient': '1296.157', 'aut_centralizer_order': 3, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 27, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.b1.a1', '18.d1.a1', '18.e1.a1', '27.b1.a1', '27.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8296, -1, 8259, -1, 8135, -1, 7739, -1], 'generators': [1, 36, 504, 6, 324, 648], 'label': '1296.157.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.23'}
id: 70719367
{'ambient': '1296.157', 'aut_centralizer_order': 2, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.2583', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.c1.a1', '18.h1.a1', '18.j1.a1', '27.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6228, -1, 6201, -1, 7328, -1, 7410, -1], 'generators': [1, 36, 84, 6, 324, 648], 'label': '1296.157.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.6'}
id: 70719368
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 72, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6755, 5609, 7279, 8778, 5639, 8425, 6613, 5588], 'generators': [324, 36, 4, 468, 648], 'label': '1296.157.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '648.77', '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': '108.17'}
id: 70719369
{'ambient': '1296.157', 'aut_centralizer_order': 216, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.48', 'aut_weyl_index': 216, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '36.a1.a1', '36.h1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3977, 8811, 4857, 5433, 4547, 5593, 4713, 8418], 'generators': [324, 36, 48, 468, 648], 'label': '1296.157.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '648.77', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719370
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.102', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '36.b1.a1', '36.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2318, -1, 4254, -1, 1870, -1, 1767, -1], 'generators': [6, 36, 648, 4, 468], 'label': '1296.157.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.c1.a1', 'projective_image': '648.77', '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': '108.25'}
id: 70719371
{'ambient': '1296.157', 'aut_centralizer_order': 4, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1944.2701', 'aut_weyl_index': 8, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '36.c1.a1', '36.d1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1301, -1, 1630, -1, 1275, -1, 532, -1], 'generators': [6, 36, 648, 84, 468], 'label': '1296.157.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '324.71'}
id: 70719372
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.102', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '36.e1.a1', '36.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5486, -1, 5455, -1, 3801, -1, 3499, -1], 'generators': [7, 36, 468, 648, 4], 'label': '1296.157.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.e1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
id: 70719373
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.28', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.f1.a1'], 'contains': ['24.c1.a1', '36.a1.a1', '36.i1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4748, -1, 3125, -1, 2825, -1, 3955, -1], 'generators': [324, 36, 100, 468, 648], 'label': '1296.157.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
id: 70719374
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.111', 'aut_weyl_index': 72, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.e1.a1'], 'contains': ['24.b1.a1', '36.e1.a1', '36.j1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3069, -1, 3645, -1, 3331, -1, 2343, -1], 'generators': [7, 36, 468, 648, 84], 'label': '1296.157.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '12.g1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
id: 70719375
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 144, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.f1.a1'], 'contains': ['24.c1.a1', '36.e1.a1', '36.k1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3526, -1, 2562, -1, 2391, -1, 2764, -1], 'generators': [7, 36, 468, 648, 496], 'label': '1296.157.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.h1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
id: 70719376
{'ambient': '1296.157', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '648.a1.a1', 'complements': ['648.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5639, 5842, 4898, 5727, 5205, 5593, 5345, 5588], 'generators': [7, 468, 84, 324, 36, 648, 4], 'label': '1296.157.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '648.77', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '648.77'}
id: 70719377
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 144, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.f1.a1'], 'contains': ['24.c1.a1', '36.e1.a1', '36.k1.a2'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3526, -1, 2192, -1, 2391, -1, 3114, -1], 'generators': [7, 36, 468, 648, 952], 'label': '1296.157.12.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.h1.a2', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a2', 'subgroup_fusion': None, 'weyl_group': '108.26'}
id: 70719378
{'ambient': '1296.157', 'aut_centralizer_order': 48, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '324.117', 'aut_weyl_index': 48, 'centralizer': '108.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [578, 742, 603, 763, 126, 660, 394, 660], 'generators': [4, 48], 'label': '1296.157.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '1296.157', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
id: 70719379
{'ambient': '1296.157', 'aut_centralizer_order': 18, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.209', 'aut_weyl_index': 162, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.f1.a1', '54.a1.a1', '54.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7503, -1, 7855, -1, 7049, -1, 7398, -1], 'generators': [6, 36, 324, 4, 648], 'label': '1296.157.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '648.77', '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': '24.6'}
id: 70719380
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.2470', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.c1.a1', '54.b1.a1', '54.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6096, -1, 6928, -1, 6112, -1, 5663, -1], 'generators': [6, 36, 324, 648, 468], 'label': '1296.157.18.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '648.77', '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': '216.35'}
id: 70719381
{'ambient': '1296.157', 'aut_centralizer_order': 4, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '432.362', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.c1.a1'], 'contains': ['36.d1.a1', '36.h1.a1', '54.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4099, -1, 5576, -1, 4929, -1, 5084, -1], 'generators': [6, 36, 324, 648, 84], 'label': '1296.157.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.c1.a1', 'projective_image': '648.77', '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': '72.6'}
id: 70719382
{'ambient': '1296.157', 'aut_centralizer_order': 18, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.209', 'aut_weyl_index': 162, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.f1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.e1.a1', '54.d1.a1', '54.f1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6573, -1, 6091, -1, 6546, -1, 6083, -1], 'generators': [7, 36, 324, 468, 648], 'label': '1296.157.18.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.d1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
id: 70719383
{'ambient': '1296.157', 'aut_centralizer_order': 108, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 324, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.g1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '54.e1.a1', '54.g1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8964, -1, 8858, -1, 8177, -1, 8233, -1], 'generators': [1, 504, 36, 324, 648], 'label': '1296.157.18.e1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.e1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719384
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.2470', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.g1.a1', '54.d1.a1', '54.h1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8024, -1, 7298, -1, 7744, -1, 7812, -1], 'generators': [7, 36, 324, 648, 4], 'label': '1296.157.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.f1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.35'}
id: 70719385
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 324, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '54.e1.a1', '54.i1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9498, -1, 9378, -1, 9242, -1, 9265, -1], 'generators': [1, 4, 36, 324, 648], 'label': '1296.157.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719386
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.362', 'aut_weyl_index': 36, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.c1.a1'], 'contains': ['36.h1.a1', '36.j1.a1', '54.d1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4633, -1, 4860, -1, 5205, -1, 5351, -1], 'generators': [7, 36, 324, 648, 84], 'label': '1296.157.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.h1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.6'}
id: 70719387
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1296.3033', 'aut_weyl_index': 12, 'centralizer': '108.a1.a1', 'complements': ['648.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.a1', '6.g1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7157, 2424, 7121, 9237, 6249, 8632, 7027, 2552], 'generators': [1, 468, 4, 48, 36, 324, 648], 'label': '1296.157.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '648.77', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
id: 70719388
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.362', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['36.i1.a1', '36.k1.a1', '36.k1.a2', '54.d1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5048, -1, 2755, -1, 4159, -1, 4337, -1], 'generators': [7, 36, 324, 648, 496], 'label': '1296.157.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '18.i1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
id: 70719389
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.15', 'aut_weyl_index': 648, 'centralizer': '18.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.c1.a1'], 'contains': ['36.h1.a1', '54.e1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6978, -1, 6487, -1, 7431, -1, 7027, -1], 'generators': [1, 648, 48, 324, 36], 'label': '1296.157.18.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.j1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719390
{'ambient': '1296.157', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '108.17', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.c1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '72.a1.a1', '72.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3037, 2818, 3672, 5892, 2431, 5593, 2846, 2997], 'generators': [648, 4, 468, 36], 'label': '1296.157.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '648.77', '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': '108.17'}
id: 70719391
{'ambient': '1296.157', 'aut_centralizer_order': 432, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 432, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.d1.a1', '12.g1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '72.c1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1125, 6002, 1816, 2619, 1621, 2761, 1079, 5827], 'generators': [648, 48, 468, 36], 'label': '1296.157.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1'], 'normal_contains': ['48.b1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '648.77', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719392
{'ambient': '1296.157', 'aut_centralizer_order': 144, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '54.8', 'aut_weyl_index': 288, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.f1.a1', '12.h1.a1', '12.h1.a2'], 'contains': ['48.c1.a1', '72.a1.a1', '72.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2097, -1, 989, -1, 1121, -1, 1826, -1], 'generators': [648, 100, 468, 36], 'label': '1296.157.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
id: 70719393
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.17', 'aut_weyl_index': 144, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '72.e1.a1', '72.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1548, -1, 1406, -1, 714, -1, 691, -1], 'generators': [6, 4, 468, 36], 'label': '1296.157.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '24.d1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
id: 70719394
{'ambient': '1296.157', 'aut_centralizer_order': 4, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '972.446', 'aut_weyl_index': 16, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.d1.a1'], 'contains': ['48.b1.a1', '72.f1.a1', '72.g1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [118, -1, 469, -1, 420, -1, 109, -1], 'generators': [6, 84, 468, 36], 'label': '1296.157.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.e1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '162.13'}
id: 70719395
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '96.209', 'aut_weyl_index': 162, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['54.a1.a1', '54.h1.a1', '54.i1.a1', '81.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9882, -1, 9885, -1, 9760, -1, 9768, -1], 'generators': [1, 4, 6, 324, 648], 'label': '1296.157.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
id: 70719396
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '96.209', 'aut_weyl_index': 162, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.c1.a1'], 'contains': ['54.b1.a1', '54.d1.a1', '54.e1.a1', '81.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8359, -1, 8287, -1, 8569, -1, 8612, -1], 'generators': [1, 36, 6, 324, 648], 'label': '1296.157.27.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '27.b1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
id: 70719397
{'ambient': '1296.157', 'aut_centralizer_order': 6, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '96.209', 'aut_weyl_index': 162, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1'], 'contains': ['54.c1.a1', '54.f1.a1', '54.g1.a1', '81.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8776, -1, 8931, -1, 8848, -1, 8883, -1], 'generators': [1, 504, 6, 324, 648], 'label': '1296.157.27.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '27.c1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
id: 70719398
{'ambient': '1296.157', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1728.30804', 'aut_weyl_index': 9, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.c1.a1', '6.d1.a1', '9.a1.a1', '9.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8276, -1, 8234, -1, 7698, -1, 7698, -1], 'generators': [1, 504, 4, 6, 36, 324, 648], 'label': '1296.157.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.35'}
id: 70719399
{'ambient': '1296.157', 'aut_centralizer_order': 648, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 648, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.f1.a1', '18.b1.a1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.a1.a1', '108.a1.a1', '108.f1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6170, 7810, 6318, 7950, 5827, 8425, 5925, 8418], 'generators': [324, 468, 36, 648], 'label': '1296.157.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1'], 'normal_contains': ['72.a1.a1', '108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '648.77', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719400
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 648, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.e1.a1', '108.b1.a1', '108.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3868, -1, 5146, -1, 4259, -1, 5154, -1], 'generators': [6, 648, 4, 36], 'label': '1296.157.36.b1.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': '36.b1.a1', 'projective_image': '648.77', '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': '12.4'}
id: 70719401
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.102', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.a1', '18.b1.a1'], 'contains': ['72.a1.a1', '72.f1.a1', '108.c1.a1', '108.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2554, -1, 3483, -1, 2976, -1, 2317, -1], 'generators': [6, 648, 468, 36], 'label': '1296.157.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '36.c1.a1', 'projective_image': '648.77', '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': '108.25'}
id: 70719402
{'ambient': '1296.157', 'aut_centralizer_order': 8, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '108.26', 'aut_weyl_index': 144, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.c1.a1'], 'contains': ['72.c1.a1', '72.g1.a1', '108.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1174, -1, 2120, -1, 2003, -1, 1450, -1], 'generators': [6, 648, 84, 36], 'label': '1296.157.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '36.d1.a1', 'projective_image': '648.77', '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': '36.4'}
id: 70719403
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 648, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.g1.a1', '12.h1.a1', '12.h1.a2', '18.d1.a1'], 'contains': ['72.a1.a1', '108.e1.a1', '108.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4913, -1, 4403, -1, 4717, -1, 3649, -1], 'generators': [7, 468, 648, 36], 'label': '1296.157.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.e1.a1', 'projective_image': '648.77', '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': '12.4'}
id: 70719404
{'ambient': '1296.157', 'aut_centralizer_order': 216, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 648, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1', '18.f1.a1', '18.g1.a1'], 'contains': ['72.b1.a1', '108.a1.a1', '108.h1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7545, -1, 7774, -1, 6873, -1, 7604, -1], 'generators': [324, 4, 36, 648], 'label': '1296.157.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '648.77', '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': '12.4'}
id: 70719405
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.102', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.f1.a1'], 'contains': ['72.b1.a1', '108.e1.a1', '108.i1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5361, -1, 5531, -1, 5409, -1, 5519, -1], 'generators': [7, 648, 4, 36], 'label': '1296.157.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.g1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
id: 70719406
{'ambient': '1296.157', 'aut_centralizer_order': 432, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1296, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.c1.a1', '18.h1.a1', '18.j1.a1'], 'contains': ['72.c1.a1', '108.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4226, -1, 4798, -1, 5102, -1, 4825, -1], 'generators': [324, 48, 648, 36], 'label': '1296.157.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.h1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719407
{'ambient': '1296.157', 'aut_centralizer_order': 216, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 1296, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.i1.a1'], 'contains': ['72.d1.a1', '108.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4507, -1, 2969, -1, 3641, -1, 4566, -1], 'generators': [324, 100, 648, 36], 'label': '1296.157.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.i1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 70719408
{'ambient': '1296.157', 'aut_centralizer_order': 24, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 144, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.h1.a1'], 'contains': ['72.c1.a1', '108.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3088, -1, 3884, -1, 3914, -1, 3267, -1], 'generators': [7, 648, 84, 36], 'label': '1296.157.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '36.j1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
id: 70719409
{'ambient': '1296.157', 'aut_centralizer_order': 1, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 3, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.e1.a1', '6.g1.a1', '9.b1.a1', '9.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6288, -1, 6303, -1, 6934, -1, 6363, -1], 'generators': [1, 504, 84, 6, 36, 324, 648], 'label': '1296.157.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.29'}
id: 70719410
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 144, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.i1.a1'], 'contains': ['72.d1.a1', '108.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3503, -1, 2689, -1, 3368, -1, 4031, -1], 'generators': [7, 648, 496, 36], 'label': '1296.157.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.k1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
id: 70719411
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 144, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a2', '18.i1.a1'], 'contains': ['72.d1.a1', '108.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3503, -1, 2403, -1, 3368, -1, 4302, -1], 'generators': [7, 648, 952, 36], 'label': '1296.157.36.k1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.k1.a2', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a2', 'subgroup_fusion': None, 'weyl_group': '108.26'}
id: 70719412
{'ambient': '1296.157', 'aut_centralizer_order': 144, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '108.17', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.d1.a1'], 'contains': ['144.a1.a1', '144.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1579, 1226, 1042, 3557, 2149, 4177, 2558, 2409], 'generators': [4, 468], 'label': '1296.157.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
id: 70719413
{'ambient': '1296.157', 'aut_centralizer_order': 432, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 432, 'centralizer': '12.b1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.e1.a1'], 'contains': ['144.a1.a1', '144.c1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [346, 3086, 469, 1646, 1615, 2522, 1079, 4062], 'generators': [48, 468], 'label': '1296.157.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.b1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '1296.157', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719414
{'ambient': '1296.157', 'aut_centralizer_order': 144, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '54.8', 'aut_weyl_index': 288, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.a1'], 'contains': ['144.a1.a1', '144.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [710, -1, 115, -1, 1193, -1, 1938, -1], 'generators': [100, 468], 'label': '1296.157.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.c1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
id: 70719415
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.11', 'aut_weyl_index': 972, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.h1.a1', '162.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7861, -1, 8082, -1, 8013, -1, 8306, -1], 'generators': [6, 324, 4, 648], 'label': '1296.157.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '648.77', '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': '8.3'}
id: 70719416
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.38', 'aut_weyl_index': 324, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.c1.a1', '162.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5991, -1, 6751, -1, 6209, -1, 6295, -1], 'generators': [6, 324, 648, 36], 'label': '1296.157.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
id: 70719417
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.38', 'aut_weyl_index': 324, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '27.c1.a1'], 'contains': ['108.d1.a1', '108.f1.a1', '162.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6937, -1, 7578, -1, 7255, -1, 6830, -1], 'generators': [6, 324, 648, 468], 'label': '1296.157.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '54.c1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
id: 70719418
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.38', 'aut_weyl_index': 324, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.f1.a1', '18.h1.a1', '18.i1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.e1.a1', '162.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6403, -1, 5957, -1, 6485, -1, 6563, -1], 'generators': [7, 324, 648, 36], 'label': '1296.157.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.d1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
id: 70719419
{'ambient': '1296.157', 'aut_centralizer_order': 216, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1944, 'centralizer': '18.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.g1.a1', '18.j1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '162.c1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8223, -1, 8433, -1, 8356, -1, 7974, -1], 'generators': [1, 36, 324, 648], 'label': '1296.157.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.e1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719420
{'ambient': '1296.157', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '648.603', 'aut_weyl_index': 24, 'centralizer': '108.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.f1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4943, 5842, 4817, 5727, 3710, 5593, 4775, 5588], 'generators': [324, 36, 468, 4, 48, 648], 'label': '1296.157.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
id: 70719421
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.11', 'aut_weyl_index': 972, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '27.c1.a1'], 'contains': ['108.f1.a1', '108.g1.a1', '162.b1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7298, -1, 7223, -1, 7598, -1, 7163, -1], 'generators': [7, 324, 504, 648], 'label': '1296.157.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '54.f1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 70719422
{'ambient': '1296.157', 'aut_centralizer_order': 216, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 648, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '27.c1.a1'], 'contains': ['108.f1.a1', '162.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9360, -1, 9407, -1, 8908, -1, 8915, -1], 'generators': [1, 324, 648, 504], 'label': '1296.157.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.g1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719423
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.38', 'aut_weyl_index': 324, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '27.a1.a1'], 'contains': ['108.h1.a1', '108.i1.a1', '162.b1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8510, -1, 8713, -1, 8629, -1, 8644, -1], 'generators': [7, 324, 648, 4], 'label': '1296.157.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.h1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
id: 70719424
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 648, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '27.a1.a1'], 'contains': ['108.h1.a1', '162.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9690, -1, 9742, -1, 9484, -1, 9474, -1], 'generators': [1, 324, 648, 4], 'label': '1296.157.54.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.i1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719425
{'ambient': '1296.157', 'aut_centralizer_order': 1296, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1296, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1', '36.c1.a1', '36.e1.a1'], 'contains': ['144.a1.a1', '216.a1.a1', '216.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2896, 5555, 2957, 5708, 3689, 5831, 3523, 6224], 'generators': [648, 468, 36], 'label': '1296.157.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '648.77', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719426
{'ambient': '1296.157', 'aut_centralizer_order': 432, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1296, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.b1.a1', '36.f1.a1', '36.g1.a1'], 'contains': ['144.b1.a1', '216.a1.a1', '216.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4060, -1, 4733, -1, 4320, -1, 4875, -1], 'generators': [648, 4, 36], 'label': '1296.157.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '648.77', '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': '12.4'}
id: 70719427
{'ambient': '1296.157', 'aut_centralizer_order': 864, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 2592, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.d1.a1', '36.h1.a1', '36.j1.a1'], 'contains': ['144.c1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1544, -1, 2168, -1, 2937, -1, 2793, -1], 'generators': [648, 48, 36], 'label': '1296.157.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.c1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719428
{'ambient': '1296.157', 'aut_centralizer_order': 432, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 2592, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.i1.a1', '36.k1.a1', '36.k1.a2'], 'contains': ['144.d1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1982, -1, 1881, -1, 2670, -1, 3852, -1], 'generators': [648, 100, 36], 'label': '1296.157.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.d1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 70719429
{'ambient': '1296.157', 'aut_centralizer_order': 36, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1296, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.b1.a1'], 'contains': ['144.b1.a1', '216.d1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2340, -1, 2519, -1, 3277, -1, 3123, -1], 'generators': [6, 4, 36], 'label': '1296.157.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.e1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 70719430
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.17', 'aut_weyl_index': 144, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '36.c1.a1'], 'contains': ['144.a1.a1', '216.e1.a1', '216.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [952, -1, 1452, -1, 2397, -1, 2317, -1], 'generators': [6, 468, 36], 'label': '1296.157.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '72.f1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
id: 70719431
{'ambient': '1296.157', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1944.2701', 'aut_weyl_index': 8, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '12.c1.a1', '12.d1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1899, -1, 2068, -1, 1275, -1, 1108, -1], 'generators': [6, 36, 468, 648, 4, 84], 'label': '1296.157.4.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '648.77', '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': '324.71'}
id: 70719432
{'ambient': '1296.157', 'aut_centralizer_order': 8, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 288, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.d1.a1'], 'contains': ['144.c1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [220, -1, 889, -1, 1930, -1, 1573, -1], 'generators': [6, 84, 36], 'label': '1296.157.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '72.g1.a1', 'projective_image': '1296.157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
id: 70719433
{'ambient': '1296.157', 'aut_centralizer_order': 12, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 972, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1', '27.c1.a1'], 'contains': ['162.a1.a1', '162.b1.a1', '162.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8769, -1, 9179, -1, 9196, -1, 9194, -1], 'generators': [1, 6], 'label': '1296.157.81.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': '648.77', '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': '8.3'}
id: 70719434
{'ambient': '1296.157', 'aut_centralizer_order': 3888, 'aut_label': '108.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3888, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.f1.a1', '36.h1.a1', '36.i1.a1', '54.b1.a1', '54.d1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '324.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5233, 6915, 5980, 7105, 5836, 7613, 5463, 8005], 'generators': [324, 36, 648], 'label': '1296.157.108.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1'], 'normal_contains': ['216.a1.a1', '324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '648.77', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.5', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 70719435
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3888, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '54.a1.a1'], 'contains': ['216.c1.a1', '216.d1.a1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4412, -1, 4752, -1, 5230, -1, 5792, -1], 'generators': [6, 648, 4], 'label': '1296.157.108.b1.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': '108.b1.a1', 'projective_image': '648.77', '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': '2.1'}
id: 70719436
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1296, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.a1', '36.d1.a1', '54.b1.a1'], 'contains': ['216.a1.a1', '216.e1.a1', '324.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2650, -1, 3346, -1, 4004, -1, 4087, -1], 'generators': [6, 648, 36], 'label': '1296.157.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '648.77', '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': '12.4'}
id: 70719437
{'ambient': '1296.157', 'aut_centralizer_order': 24, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1296, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '54.c1.a1'], 'contains': ['216.b1.a1', '216.f1.a1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3539, -1, 4428, -1, 4635, -1, 4299, -1], 'generators': [6, 648, 468], 'label': '1296.157.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '108.d1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719438
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1296, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.g1.a1', '36.j1.a1', '36.k1.a1', '36.k1.a2', '54.d1.a1'], 'contains': ['216.a1.a1', '324.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4047, -1, 3936, -1, 4884, -1, 4540, -1], 'generators': [7, 648, 36], 'label': '1296.157.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.e1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 70719439
{'ambient': '1296.157', 'aut_centralizer_order': 1296, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3888, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.c1.a1', '54.f1.a1', '54.g1.a1'], 'contains': ['216.b1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7094, -1, 7064, -1, 7137, -1, 6716, -1], 'generators': [324, 468, 648], 'label': '1296.157.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.f1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 70719440
{'ambient': '1296.157', 'aut_centralizer_order': 72, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3888, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '54.f1.a1'], 'contains': ['216.b1.a1', '324.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5515, -1, 6253, -1, 5569, -1, 5204, -1], 'generators': [7, 504, 648], 'label': '1296.157.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1.a1', 'old_label': '108.g1.a1', 'projective_image': '648.77', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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