LMFDB - Abstract group data

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [2, 6, 18, 12, 18], 'aut_gens': [[1, 12, 24, 432], [625, 396, 3738, 3456], [403, 540, 1722, 2160], [1021, 3660, 1752, 3456], [1921, 108, 1380, 96], [3667, 588, 3066, 3024]], 'aut_group': None, 'aut_hash': 6413894936646692975, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7776, 'aut_permdeg': 81, 'aut_perms': [2348626444192077470115448864968660989412900985105600723942827890908666406293686957517518915599176462791021402239261751095, 8211684038401700553277439321149232852572937170010788039147440802284586531199700070596131664598898597884290588814985942, 539038189916907611635091614443638530575156267284042636016175034674159432635497925030580296549722007890950807515294762103, 1095506853349790590068897062593826261559004894865550219066203458268170037971352846011727776451131959348154879902416653330, 5414842381195339002097546086664891941185549906322547034165147497921904605046460476686523212083710270050051919408741234340], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 2, 1], [2, 81, 1, 2], [3, 4, 1, 2], [3, 9, 1, 2], [4, 18, 2, 1], [4, 162, 2, 1], [6, 4, 1, 2], [6, 9, 1, 2], [6, 36, 2, 1], [6, 54, 2, 2], [6, 81, 1, 4], [9, 12, 1, 2], [9, 24, 1, 2], [9, 36, 1, 4], [12, 36, 2, 1], [12, 54, 2, 2], [12, 162, 2, 2], [18, 12, 1, 2], [18, 24, 1, 2], [18, 36, 1, 4], [18, 108, 2, 3], [36, 108, 2, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_9:D_9.C_6.C_2^3', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '1944.2315', 'autcentquo_hash': 2315, 'autcentquo_nilpotent': False, 'autcentquo_order': 1944, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_9^2:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 18, 2], [2, 81, 2], [3, 4, 2], [3, 9, 2], [4, 18, 2], [4, 162, 2], [6, 4, 2], [6, 9, 2], [6, 36, 2], [6, 54, 4], [6, 81, 4], [9, 12, 2], [9, 24, 2], [9, 36, 4], [12, 36, 2], [12, 54, 4], [12, 162, 4], [18, 12, 2], [18, 24, 2], [18, 36, 4], [18, 108, 6], [36, 108, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1944.2315', 'commutator_count': 1, 'commutator_label': '162.16', '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', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 183, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 2], [2, 81, 1, 2], [3, 4, 1, 2], [3, 9, 2, 1], [4, 18, 2, 1], [4, 162, 2, 1], [6, 4, 1, 2], [6, 9, 2, 1], [6, 36, 1, 2], [6, 54, 2, 2], [6, 81, 2, 2], [9, 12, 1, 2], [9, 24, 1, 2], [9, 36, 2, 2], [12, 36, 2, 1], [12, 54, 4, 1], [12, 162, 4, 1], [18, 12, 1, 2], [18, 24, 1, 2], [18, 36, 2, 2], [18, 108, 1, 2], [18, 108, 2, 2], [36, 108, 2, 1], [36, 108, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 576, 'exponent': 36, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2], [12, 1, 2], [24, 1, 2]], 'familial': False, 'frattini_label': '18.5', 'frattini_quotient': '216.157', 'hash': 2065347936632301655, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [12, 2, 18, 9], 'inner_gens': [[1, 1308, 900, 336], [2593, 12, 2568, 3456], [2653, 1788, 24, 3456], [529, 876, 888, 432]], 'inner_hash': 2315, 'inner_nilpotent': False, 'inner_order': 1944, 'inner_split': True, 'inner_tex': 'D_9^2:C_6', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 24], [2, 6], [4, 24], [12, 8], [24, 4]], 'label': '3888.ha', 'linC_count': 4, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'D9^2:C12', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 49, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 66, 'number_divisions': 41, 'number_normal_subgroups': 28, 'number_subgroup_autclasses': 251, 'number_subgroup_classes': 290, 'number_subgroups': 5962, 'old_label': None, 'order': 3888, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 199], [3, 26], [4, 360], [6, 638], [9, 216], [12, 936], [18, 864], [36, 648]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [2224, 1318], 'outer_gens': [[2065, 108, 990, 48], [1063, 2844, 264, 3024]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 10], [8, 7], [12, 6], [16, 1], [24, 5]], 'representations': {'PC': {'code': '19410226756915649048442451470710299612759530148642196977374460301284966159214087519793800415830405921155671631', 'gens': [1, 4, 5, 8], 'pres': [9, 2, 2, 3, 2, 2, 3, 3, 3, 3, 18, 46, 47091, 26148, 40504, 54553, 32692, 9661, 130, 186629, 2606, 2615, 1760, 212, 163302, 9087, 1545, 24199, 31120, 31129, 20770, 10411, 286, 11672, 104993, 17531, 8792]}, 'Perm': {'d': 22, 'gens': [56220729215984489649, 102572492183443659609]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_9^2:C_{12}', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}

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

gps_conj_classes • Show schema

id: 161039166
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 183, 'group_order': 3888, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 161039177
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 183, 'group_order': 3888, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 2898, 'size': 1}
id: 161039188
{'aut_label': '2B', 'centralizer': '18.b1.a1', 'counter': 3, 'group_counter': 183, 'group_order': 3888, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 2808, 'size': 18}
id: 161039199
{'aut_label': '2B', 'centralizer': '18.b1.a1', 'counter': 4, 'group_counter': 183, 'group_order': 3888, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 1902, 'size': 18}
id: 161039210
{'aut_label': '2D', 'centralizer': '81.a1.a1', 'counter': 5, 'group_counter': 183, 'group_order': 3888, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 2214, 'size': 81}
id: 161039221
{'aut_label': '2E', 'centralizer': '81.a1.a1', 'counter': 6, 'group_counter': 183, 'group_order': 3888, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 156, 'size': 81}
id: 161039229
{'aut_label': '3A', 'centralizer': '4.c1.a1', 'counter': 7, 'group_counter': 183, 'group_order': 3888, 'label': '3A', 'order': 3, 'powers': [7, 1], 'representative': 2592, 'size': 4}
id: 161039230
{'aut_label': '3B', 'centralizer': '4.d1.a1', 'counter': 8, 'group_counter': 183, 'group_order': 3888, 'label': '3B', 'order': 3, 'powers': [8, 1], 'representative': 2880, 'size': 4}
id: 161039231
{'aut_label': '3C1', 'centralizer': '9.a1.a1', 'counter': 9, 'group_counter': 183, 'group_order': 3888, 'label': '3C1', 'order': 3, 'powers': [10, 1], 'representative': 1448, 'size': 9}
id: 161039167
{'aut_label': '3C-1', 'centralizer': '9.a1.a1', 'counter': 10, 'group_counter': 183, 'group_order': 3888, 'label': '3C-1', 'order': 3, 'powers': [9, 1], 'representative': 2884, 'size': 9}
id: 161039168
{'aut_label': '4A1', 'centralizer': '18.f1.a1', 'counter': 11, 'group_counter': 183, 'group_order': 3888, 'label': '4A1', 'order': 4, 'powers': [2, 12], 'representative': 1323, 'size': 18}
id: 161039169
{'aut_label': '4A1', 'centralizer': '18.f1.a1', 'counter': 12, 'group_counter': 183, 'group_order': 3888, 'label': '4A-1', 'order': 4, 'powers': [2, 11], 'representative': 2925, 'size': 18}
id: 161039170
{'aut_label': '4B1', 'centralizer': '162.d1.a1', 'counter': 13, 'group_counter': 183, 'group_order': 3888, 'label': '4B1', 'order': 4, 'powers': [5, 14], 'representative': 2325, 'size': 162}
id: 161039171
{'aut_label': '4B1', 'centralizer': '162.d1.a1', 'counter': 14, 'group_counter': 183, 'group_order': 3888, 'label': '4B-1', 'order': 4, 'powers': [5, 13], 'representative': 1359, 'size': 162}
id: 161039172
{'aut_label': '6A', 'centralizer': '4.c1.a1', 'counter': 15, 'group_counter': 183, 'group_order': 3888, 'label': '6A', 'order': 6, 'powers': [7, 2], 'representative': 306, 'size': 4}
id: 161039173
{'aut_label': '6B', 'centralizer': '4.d1.a1', 'counter': 16, 'group_counter': 183, 'group_order': 3888, 'label': '6B', 'order': 6, 'powers': [8, 2], 'representative': 18, 'size': 4}
id: 161039174
{'aut_label': '6C1', 'centralizer': '9.a1.a1', 'counter': 17, 'group_counter': 183, 'group_order': 3888, 'label': '6C1', 'order': 6, 'powers': [10, 2], 'representative': 14, 'size': 9}
id: 161039175
{'aut_label': '6C-1', 'centralizer': '9.a1.a1', 'counter': 18, 'group_counter': 183, 'group_order': 3888, 'label': '6C-1', 'order': 6, 'powers': [9, 2], 'representative': 1462, 'size': 9}
id: 161039176
{'aut_label': '6D', 'centralizer': '36.a1.a1', 'counter': 19, 'group_counter': 183, 'group_order': 3888, 'label': '6D', 'order': 6, 'powers': [7, 3], 'representative': 3384, 'size': 36}
id: 161039178
{'aut_label': '6D', 'centralizer': '36.a1.a1', 'counter': 20, 'group_counter': 183, 'group_order': 3888, 'label': '6E', 'order': 6, 'powers': [7, 4], 'representative': 1530, 'size': 36}
id: 161039179
{'aut_label': '6F1', 'centralizer': '54.a1.a1', 'counter': 21, 'group_counter': 183, 'group_order': 3888, 'label': '6F1', 'order': 6, 'powers': [9, 3], 'representative': 76, 'size': 54}
id: 161039180
{'aut_label': '6F-1', 'centralizer': '54.a1.a1', 'counter': 22, 'group_counter': 183, 'group_order': 3888, 'label': '6F-1', 'order': 6, 'powers': [10, 3], 'representative': 80, 'size': 54}
id: 161039181
{'aut_label': '6F-1', 'centralizer': '54.a1.a1', 'counter': 23, 'group_counter': 183, 'group_order': 3888, 'label': '6G1', 'order': 6, 'powers': [10, 4], 'representative': 458, 'size': 54}
id: 161039182
{'aut_label': '6F1', 'centralizer': '54.a1.a1', 'counter': 24, 'group_counter': 183, 'group_order': 3888, 'label': '6G-1', 'order': 6, 'powers': [9, 4], 'representative': 466, 'size': 54}
id: 161039183
{'aut_label': '6H1', 'centralizer': '81.a1.a1', 'counter': 25, 'group_counter': 183, 'group_order': 3888, 'label': '6H1', 'order': 6, 'powers': [10, 5], 'representative': 1058, 'size': 81}
id: 161039184
{'aut_label': '6H-1', 'centralizer': '81.a1.a1', 'counter': 26, 'group_counter': 183, 'group_order': 3888, 'label': '6H-1', 'order': 6, 'powers': [9, 5], 'representative': 3802, 'size': 81}
id: 161039185
{'aut_label': '6I1', 'centralizer': '81.a1.a1', 'counter': 27, 'group_counter': 183, 'group_order': 3888, 'label': '6I1', 'order': 6, 'powers': [9, 6], 'representative': 160, 'size': 81}
id: 161039186
{'aut_label': '6I-1', 'centralizer': '81.a1.a1', 'counter': 28, 'group_counter': 183, 'group_order': 3888, 'label': '6I-1', 'order': 6, 'powers': [10, 6], 'representative': 164, 'size': 81}
id: 161039187
{'aut_label': '9A', 'centralizer': '12.f1.a1', 'counter': 29, 'group_counter': 183, 'group_order': 3888, 'label': '9A', 'order': 9, 'powers': [29, 7], 'representative': 3456, 'size': 12}
id: 161039189
{'aut_label': '9B', 'centralizer': '12.k1.a1', 'counter': 30, 'group_counter': 183, 'group_order': 3888, 'label': '9B', 'order': 9, 'powers': [30, 8], 'representative': 672, 'size': 12}
id: 161039190
{'aut_label': '9C', 'centralizer': '24.a1.a1', 'counter': 31, 'group_counter': 183, 'group_order': 3888, 'label': '9C', 'order': 9, 'powers': [31, 7], 'representative': 3744, 'size': 24}
id: 161039191
{'aut_label': '9D', 'centralizer': '24.a1.a1', 'counter': 32, 'group_counter': 183, 'group_order': 3888, 'label': '9D', 'order': 9, 'powers': [32, 8], 'representative': 3840, 'size': 24}
id: 161039192
{'aut_label': '9E1', 'centralizer': '36.d1.a1', 'counter': 33, 'group_counter': 183, 'group_order': 3888, 'label': '9E1', 'order': 9, 'powers': [34, 7], 'representative': 2452, 'size': 36}
id: 161039193
{'aut_label': '9E-1', 'centralizer': '36.d1.a1', 'counter': 34, 'group_counter': 183, 'group_order': 3888, 'label': '9E-1', 'order': 9, 'powers': [33, 7], 'representative': 584, 'size': 36}
id: 161039194
{'aut_label': '9F1', 'centralizer': '36.p1.a1', 'counter': 35, 'group_counter': 183, 'group_order': 3888, 'label': '9F1', 'order': 9, 'powers': [36, 8], 'representative': 3272, 'size': 36}
id: 161039195
{'aut_label': '9F-1', 'centralizer': '36.p1.a1', 'counter': 36, 'group_counter': 183, 'group_order': 3888, 'label': '9F-1', 'order': 9, 'powers': [35, 8], 'representative': 3796, 'size': 36}
id: 161039196
{'aut_label': '12A1', 'centralizer': '36.r1.a1', 'counter': 37, 'group_counter': 183, 'group_order': 3888, 'label': '12A1', 'order': 12, 'powers': [16, 12], 'representative': 1467, 'size': 36}
id: 161039197
{'aut_label': '12A1', 'centralizer': '36.r1.a1', 'counter': 38, 'group_counter': 183, 'group_order': 3888, 'label': '12A-1', 'order': 12, 'powers': [16, 11], 'representative': 333, 'size': 36}
id: 161039198
{'aut_label': '12B1', 'centralizer': '54.d1.a1', 'counter': 39, 'group_counter': 183, 'group_order': 3888, 'label': '12B1', 'order': 12, 'powers': [17, 11], 'representative': 37, 'size': 54}
id: 161039200
{'aut_label': '12B-1', 'centralizer': '54.d1.a1', 'counter': 40, 'group_counter': 183, 'group_order': 3888, 'label': '12B-1', 'order': 12, 'powers': [18, 12], 'representative': 35, 'size': 54}
id: 161039201
{'aut_label': '12B-1', 'centralizer': '54.d1.a1', 'counter': 41, 'group_counter': 183, 'group_order': 3888, 'label': '12B5', 'order': 12, 'powers': [18, 11], 'representative': 41, 'size': 54}
id: 161039202
{'aut_label': '12B1', 'centralizer': '54.d1.a1', 'counter': 42, 'group_counter': 183, 'group_order': 3888, 'label': '12B-5', 'order': 12, 'powers': [17, 12], 'representative': 31, 'size': 54}
id: 161039203
{'aut_label': '12C1', 'centralizer': '162.d1.a1', 'counter': 43, 'group_counter': 183, 'group_order': 3888, 'label': '12C1', 'order': 12, 'powers': [25, 13], 'representative': 355, 'size': 162}
id: 161039204
{'aut_label': '12C-1', 'centralizer': '162.d1.a1', 'counter': 44, 'group_counter': 183, 'group_order': 3888, 'label': '12C-1', 'order': 12, 'powers': [26, 14], 'representative': 881, 'size': 162}
id: 161039205
{'aut_label': '12C-1', 'centralizer': '162.d1.a1', 'counter': 45, 'group_counter': 183, 'group_order': 3888, 'label': '12C5', 'order': 12, 'powers': [26, 13], 'representative': 2807, 'size': 162}
id: 161039206
{'aut_label': '12C1', 'centralizer': '162.d1.a1', 'counter': 46, 'group_counter': 183, 'group_order': 3888, 'label': '12C-5', 'order': 12, 'powers': [25, 14], 'representative': 3757, 'size': 162}
id: 161039207
{'aut_label': '18A', 'centralizer': '12.f1.a1', 'counter': 47, 'group_counter': 183, 'group_order': 3888, 'label': '18A', 'order': 18, 'powers': [29, 15], 'representative': 738, 'size': 12}
id: 161039208
{'aut_label': '18B', 'centralizer': '12.k1.a1', 'counter': 48, 'group_counter': 183, 'group_order': 3888, 'label': '18B', 'order': 18, 'powers': [30, 16], 'representative': 1074, 'size': 12}
id: 161039209
{'aut_label': '18C', 'centralizer': '24.a1.a1', 'counter': 49, 'group_counter': 183, 'group_order': 3888, 'label': '18C', 'order': 18, 'powers': [31, 15], 'representative': 450, 'size': 24}
id: 161039211
{'aut_label': '18D', 'centralizer': '24.a1.a1', 'counter': 50, 'group_counter': 183, 'group_order': 3888, 'label': '18D', 'order': 18, 'powers': [32, 16], 'representative': 498, 'size': 24}
id: 161039212
{'aut_label': '18E1', 'centralizer': '36.d1.a1', 'counter': 51, 'group_counter': 183, 'group_order': 3888, 'label': '18E1', 'order': 18, 'powers': [33, 15], 'representative': 446, 'size': 36}
id: 161039213
{'aut_label': '18E-1', 'centralizer': '36.d1.a1', 'counter': 52, 'group_counter': 183, 'group_order': 3888, 'label': '18E-1', 'order': 18, 'powers': [34, 15], 'representative': 454, 'size': 36}
id: 161039214
{'aut_label': '18F1', 'centralizer': '36.p1.a1', 'counter': 53, 'group_counter': 183, 'group_order': 3888, 'label': '18F1', 'order': 18, 'powers': [35, 16], 'representative': 1222, 'size': 36}
id: 161039215
{'aut_label': '18F-1', 'centralizer': '36.p1.a1', 'counter': 54, 'group_counter': 183, 'group_order': 3888, 'label': '18F-1', 'order': 18, 'powers': [36, 16], 'representative': 3422, 'size': 36}
id: 161039216
{'aut_label': '18G', 'centralizer': '108.b1.a1', 'counter': 55, 'group_counter': 183, 'group_order': 3888, 'label': '18G', 'order': 18, 'powers': [29, 19], 'representative': 2244, 'size': 108}
id: 161039217
{'aut_label': '18G', 'centralizer': '108.b1.a1', 'counter': 56, 'group_counter': 183, 'group_order': 3888, 'label': '18H', 'order': 18, 'powers': [29, 20], 'representative': 3738, 'size': 108}
id: 161039218
{'aut_label': '18I1', 'centralizer': '108.c1.a1', 'counter': 57, 'group_counter': 183, 'group_order': 3888, 'label': '18I1', 'order': 18, 'powers': [34, 19], 'representative': 3292, 'size': 108}
id: 161039219
{'aut_label': '18I-1', 'centralizer': '108.c1.a1', 'counter': 58, 'group_counter': 183, 'group_order': 3888, 'label': '18I-1', 'order': 18, 'powers': [33, 19], 'representative': 3344, 'size': 108}
id: 161039220
{'aut_label': '18I1', 'centralizer': '108.c1.a1', 'counter': 59, 'group_counter': 183, 'group_order': 3888, 'label': '18J1', 'order': 18, 'powers': [34, 20], 'representative': 3022, 'size': 108}
id: 161039222
{'aut_label': '18I-1', 'centralizer': '108.c1.a1', 'counter': 60, 'group_counter': 183, 'group_order': 3888, 'label': '18J-1', 'order': 18, 'powers': [33, 20], 'representative': 326, 'size': 108}
id: 161039223
{'aut_label': '36A1', 'centralizer': '108.q1.a1', 'counter': 61, 'group_counter': 183, 'group_order': 3888, 'label': '36A1', 'order': 36, 'powers': [48, 37], 'representative': 1197, 'size': 108}
id: 161039224
{'aut_label': '36A1', 'centralizer': '108.q1.a1', 'counter': 62, 'group_counter': 183, 'group_order': 3888, 'label': '36A-1', 'order': 36, 'powers': [48, 38], 'representative': 1419, 'size': 108}
id: 161039225
{'aut_label': '36B1', 'centralizer': '108.r1.a1', 'counter': 63, 'group_counter': 183, 'group_order': 3888, 'label': '36B1', 'order': 36, 'powers': [53, 37], 'representative': 713, 'size': 108}
id: 161039226
{'aut_label': '36B-1', 'centralizer': '108.r1.a1', 'counter': 64, 'group_counter': 183, 'group_order': 3888, 'label': '36B-1', 'order': 36, 'powers': [54, 38], 'representative': 3823, 'size': 108}
id: 161039227
{'aut_label': '36B-1', 'centralizer': '108.r1.a1', 'counter': 65, 'group_counter': 183, 'group_order': 3888, 'label': '36B5', 'order': 36, 'powers': [54, 37], 'representative': 3829, 'size': 108}
id: 161039228
{'aut_label': '36B1', 'centralizer': '108.r1.a1', 'counter': 66, 'group_counter': 183, 'group_order': 3888, 'label': '36B-5', 'order': 36, 'powers': [53, 38], 'representative': 707, 'size': 108}

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: 15868759
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 15868770
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 15868781
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 15868792
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 15868795
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1], 'schur_index': 1}
id: 15868796
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868797
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868798
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, -1, -1, -2, -2, 2, 2, 2, 2, -1, -1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1], 'schur_index': 1}
id: 15868799
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, -1, -1, 2, 2, -2, -2, 2, 2, -1, -1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, -1, -1, -1, -1, -2, -2, 1, 1, 1, 1, 2, 2, -1, -1, -1, -1], 'schur_index': 1}
id: 15868760
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -2, -2, -2, -2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -2, -2, 1, 1, 1, 1], 'schur_index': 1}
id: 15868763
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, -2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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: 15868764
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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: 15868761
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1k', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 4, 4, -2, -2, 0, 0, 0, 0, -4, -4, 2, 2, -4, 4, 2, 2, -2, -2, 2, 2, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, -4, 4, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868762
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.1l', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 4, 4, -2, -2, 0, 0, 0, 0, -4, -4, 2, 2, 4, -4, -2, -2, 2, 2, 2, 2, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, 4, -4, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868765
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.2c', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, -4, 4, 4, -2, -2, 0, 0, 0, 0, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 4, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868766
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.2d', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -4, -4, 4, 4, -2, -2, 0, 0, 0, 0, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 4, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868767
{'cdim': 4, 'counter': 17, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4a', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 2, 2, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, 1, -2, -2, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, 1, -2, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 15868768
{'cdim': 4, 'counter': 18, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4b', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 2, 2, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, -2, -2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868769
{'cdim': 4, 'counter': 19, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4c', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, -2, -2, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868771
{'cdim': 4, 'counter': 20, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4d', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, 1, -2, -2, 1, 1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, 1, -2, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 15868772
{'cdim': 4, 'counter': 21, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4e', 'multiplicity': 1, 'nt': [12, 79], 'qdim': 4, 'qvalues': [4, -4, -2, 2, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, -4, -4, -4, -4, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, 2, 2, 1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868773
{'cdim': 4, 'counter': 22, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4f', 'multiplicity': 1, 'nt': [12, 79], 'qdim': 4, 'qvalues': [4, -4, 2, -2, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, -4, -4, -4, -4, 2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, 2, 2, -1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868774
{'cdim': 4, 'counter': 23, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4g', 'multiplicity': 2, 'nt': [12, 121], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 8, 8, -4, -4, 4, 4, 0, 0, 8, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -4, 2, 2, 2, -1, -1, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, -4, 2, -4, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 1, 1], 'schur_index': 1}
id: 15868775
{'cdim': 4, 'counter': 24, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4h', 'multiplicity': 2, 'nt': [12, 121], 'qdim': 8, 'qvalues': [8, 8, 4, 4, 0, 0, 8, 8, -4, -4, 0, 0, 0, 0, 8, 8, -4, -4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 2, -4, 2, -4, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, -4, -1, -1, 2, 2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868776
{'cdim': 4, 'counter': 25, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4i', 'multiplicity': 2, 'nt': [24, 213], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -4, 2, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 4, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868777
{'cdim': 4, 'counter': 26, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4j', 'multiplicity': 2, 'nt': [24, 561], 'qdim': 8, 'qvalues': [8, 8, -4, -4, 0, 0, 8, 8, -4, -4, 0, 0, 0, 0, 8, 8, -4, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 2, -4, 2, -4, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, -4, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868778
{'cdim': 4, 'counter': 27, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4k', 'multiplicity': 2, 'nt': [24, 561], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 8, 8, -4, -4, -4, -4, 0, 0, 8, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -4, 2, 2, 2, -1, -1, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, -4, 2, -4, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, -1, -1], 'schur_index': 1}
id: 15868779
{'cdim': 4, 'counter': 28, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4l', 'multiplicity': 2, 'nt': [24, 1317], 'qdim': 8, 'qvalues': [8, -8, -4, 4, 0, 0, 8, 8, -4, -4, 0, 0, 0, 0, -8, -8, 4, 4, -4, 4, 2, 2, -2, -2, 0, 0, 0, 0, 2, -4, 2, -4, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, 1, 1, -2, -2, 2, -2, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868780
{'cdim': 4, 'counter': 29, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4m', 'multiplicity': 2, 'nt': [24, 1317], 'qdim': 8, 'qvalues': [8, -8, 4, -4, 0, 0, 8, 8, -4, -4, 0, 0, 0, 0, -8, -8, 4, 4, 4, -4, -2, -2, 2, 2, 0, 0, 0, 0, 2, -4, 2, -4, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, 1, 1, -2, -2, -2, 2, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868783
{'cdim': 12, 'counter': 31, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.12a', 'multiplicity': 1, 'nt': [18, 338], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, -6, 3, 0, 0, 6, 6, 0, 0, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868784
{'cdim': 12, 'counter': 32, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.12b', 'multiplicity': 1, 'nt': [18, 338], 'qdim': 12, 'qvalues': [12, 12, 6, 6, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868785
{'cdim': 12, 'counter': 33, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.12c', 'multiplicity': 1, 'nt': [36, 2745], 'qdim': 12, 'qvalues': [12, 12, -6, -6, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868786
{'cdim': 12, 'counter': 34, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.12d', 'multiplicity': 1, 'nt': [36, 2745], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, -6, 3, 0, 0, -6, -6, 0, 0, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868787
{'cdim': 12, 'counter': 35, 'faithful': True, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.12e', 'multiplicity': 1, 'nt': [36, 4674], 'qdim': 12, 'qvalues': [12, -12, -6, 6, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868788
{'cdim': 12, 'counter': 36, 'faithful': True, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.12f', 'multiplicity': 1, 'nt': [36, 4674], 'qdim': 12, 'qvalues': [12, -12, 6, -6, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868782
{'cdim': 4, 'counter': 30, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.4n', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 16, 16, -8, -8, 0, 0, 0, 0, -16, -16, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, -8, 4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, 8, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868789
{'cdim': 12, 'counter': 37, 'faithful': True, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.12g', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, -12, 6, 0, 0, 0, 0, 0, 0, 12, -6, 0, 0, 0, 0, 0, 0, 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, -12, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868790
{'cdim': 24, 'counter': 38, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.24a', 'multiplicity': 1, 'nt': [36, 2919], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 0, 0, -12, 6, 0, 0, 0, 0, 0, 0, -12, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868791
{'cdim': 24, 'counter': 39, 'faithful': False, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.24b', 'multiplicity': 1, 'nt': [36, 2919], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 0, 0, 6, -12, 0, 0, 0, 0, 0, 0, 6, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868793
{'cdim': 24, 'counter': 40, 'faithful': True, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.24c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, -12, 6, 0, 0, 0, 0, 0, 0, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 15868794
{'cdim': 24, 'counter': 41, 'faithful': True, 'group': '3888.ha', 'group_order': 3888, 'image': None, 'label': '3888.ha.24d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, 6, -12, 0, 0, 0, 0, 0, 0, -6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 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: 35866833
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 3888, 'label': '3888.ha.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 35866844
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 1944, 'label': '3888.ha.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 35866855
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 1944, 'label': '3888.ha.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 35866866
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 1944, 'label': '3888.ha.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 35866877
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 1296, 'label': '3888.ha.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
id: 35866888
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 1296, 'label': '3888.ha.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
id: 35866896
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 972, 'label': '3888.ha.1f1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
id: 35866897
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 972, 'label': '3888.ha.1f2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
id: 35866898
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 972, 'label': '3888.ha.1g1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
id: 35866834
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 972, 'label': '3888.ha.1g2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
id: 35866835
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 648, 'label': '3888.ha.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
id: 35866836
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 648, 'label': '3888.ha.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
id: 35866837
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 648, 'label': '3888.ha.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
id: 35866838
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 648, 'label': '3888.ha.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
id: 35866839
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 648, 'label': '3888.ha.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
id: 35866840
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 648, 'label': '3888.ha.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
id: 35866841
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 17, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.b1', 'kernel_order': 324, 'label': '3888.ha.1k1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]]]}
id: 35866842
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 18, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.b1', 'kernel_order': 324, 'label': '3888.ha.1k2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]]]}
id: 35866843
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 19, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.b1', 'kernel_order': 324, 'label': '3888.ha.1k3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]]]}
id: 35866845
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 20, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.b1', 'kernel_order': 324, 'label': '3888.ha.1k4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]]]}
id: 35866846
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 21, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 324, 'label': '3888.ha.1l1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]]]}
id: 35866847
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 22, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 324, 'label': '3888.ha.1l2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]]]}
id: 35866848
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 23, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 324, 'label': '3888.ha.1l3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]]]}
id: 35866849
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 3888, 'counter': 24, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 324, 'label': '3888.ha.1l4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]]]}
id: 35866850
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 972, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 486, 'label': '3888.ha.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 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]], [[0, 0]], [[0, 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]], [[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]], [[-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: 35866851
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 972, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 486, 'label': '3888.ha.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 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]], [[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]], [[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: 35866852
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 972, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 162, 'label': '3888.ha.2c1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-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]]]}
id: 35866853
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 972, 'counter': 28, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 162, 'label': '3888.ha.2c2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-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]]]}
id: 35866854
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 972, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 162, 'label': '3888.ha.2d1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[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]]]}
id: 35866856
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 972, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 162, 'label': '3888.ha.2d2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[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]]]}
id: 35866857
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 54, 'label': '3888.ha.4a', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 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, 0]], [[-1, 0]]]}
id: 35866858
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 54, 'label': '3888.ha.4b', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 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]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866859
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 33, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 54, 'label': '3888.ha.4c', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 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]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866860
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 34, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 54, 'label': '3888.ha.4d', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 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, 0]], [[1, 0]]]}
id: 35866861
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '144.115', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 27, 'label': '3888.ha.4e', 'nt': [12, 79], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 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]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866862
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 36, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '144.115', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 27, 'label': '3888.ha.4f', 'nt': [12, 79], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 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]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866863
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 37, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '216.157', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 18, 'label': '3888.ha.4g1', 'nt': [12, 121], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
id: 35866864
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 38, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '216.157', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 18, 'label': '3888.ha.4g2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
id: 35866865
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 39, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '216.157', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 18, 'label': '3888.ha.4h1', 'nt': [12, 121], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866867
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 40, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '216.157', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 18, 'label': '3888.ha.4h2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866868
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 41, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '144.115', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 27, 'label': '3888.ha.4i1', 'nt': [24, 213], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
id: 35866869
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 42, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '144.115', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 27, 'label': '3888.ha.4i2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
id: 35866870
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 43, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '216.157', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 18, 'label': '3888.ha.4j1', 'nt': [24, 561], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866871
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 44, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '216.157', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 18, 'label': '3888.ha.4j2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866872
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 45, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '216.157', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 18, 'label': '3888.ha.4k1', 'nt': [24, 561], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
id: 35866873
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 46, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '216.157', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 18, 'label': '3888.ha.4k2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
id: 35866874
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 47, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '432.574', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 9, 'label': '3888.ha.4l1', 'nt': [24, 1317], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, -1]], [[-4, 1]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866875
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 48, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '432.574', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 9, 'label': '3888.ha.4l2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 1]], [[-4, -1]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866876
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 49, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '432.574', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 9, 'label': '3888.ha.4m1', 'nt': [24, 1317], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, -1]], [[-4, 1]], [[2, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866878
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 50, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '432.574', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 9, 'label': '3888.ha.4m2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 1]], [[-4, -1]], [[2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866879
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 51, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '432.574', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 9, 'label': '3888.ha.4n1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 2]], [[4, 4]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 2]], [[-4, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 4]], [[2, 2]], [[-1, 2]], [[1, 4]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 2]], [[2, 4]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]]]}
id: 35866880
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 52, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '432.574', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 9, 'label': '3888.ha.4n2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 4]], [[-4, 2]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 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]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 2]], [[-2, 4]], [[1, 4]], [[-1, 2]], [[2, 3]], [[-2, 3]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 4]], [[-2, 2]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]]]}
id: 35866881
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 53, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '432.574', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 9, 'label': '3888.ha.4n3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 2]], [[4, 4]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 2]], [[-4, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 4]], [[2, 2]], [[-1, 2]], [[1, 4]], [[2, 3]], [[-2, 3]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 2]], [[2, 4]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]]]}
id: 35866882
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 54, 'counter': 54, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '432.574', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 9, 'label': '3888.ha.4n4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 4]], [[-4, 2]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 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]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 2]], [[-2, 4]], [[1, 4]], [[-1, 2]], [[-2, 3]], [[2, 3]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 4]], [[-2, 2]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]]]}
id: 35866883
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 55, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '1944.2315', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1.a1', 'kernel_order': 2, 'label': '3888.ha.12a', 'nt': [18, 338], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866884
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 56, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '1944.2315', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1.a1', 'kernel_order': 2, 'label': '3888.ha.12b', 'nt': [18, 338], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866885
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 57, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '1944.2315', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1.a1', 'kernel_order': 2, 'label': '3888.ha.12c', 'nt': [36, 2745], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866886
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 58, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '1944.2315', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1.a1', 'kernel_order': 2, 'label': '3888.ha.12d', 'nt': [36, 2745], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866887
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 59, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.ha', 'image_order': 3888, 'indicator': 1, 'kernel': '3888.a1.a1', 'kernel_order': 1, 'label': '3888.ha.12e', 'nt': [36, 4674], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866889
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 60, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.ha', 'image_order': 3888, 'indicator': 1, 'kernel': '3888.a1.a1', 'kernel_order': 1, 'label': '3888.ha.12f', 'nt': [36, 4674], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866890
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 61, 'cyclotomic_n': 4, 'dim': 12, 'faithful': True, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.ha', 'image_order': 3888, 'indicator': 0, 'kernel': '3888.a1.a1', 'kernel_order': 1, 'label': '3888.ha.12g1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[6, 1]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866891
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 62, 'cyclotomic_n': 4, 'dim': 12, 'faithful': True, 'field': [1, 0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.ha', 'image_order': 3888, 'indicator': 0, 'kernel': '3888.a1.a1', 'kernel_order': 1, 'label': '3888.ha.12g2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[-6, 1]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866892
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 63, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '1944.2315', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1.a1', 'kernel_order': 2, 'label': '3888.ha.24a', 'nt': [36, 2919], 'q_character': None, 'values': [[[24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866893
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 64, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '1944.2315', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1.a1', 'kernel_order': 2, 'label': '3888.ha.24b', 'nt': [36, 2919], 'q_character': None, 'values': [[[24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866894
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 65, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.ha', 'image_order': 3888, 'indicator': 1, 'kernel': '3888.a1.a1', 'kernel_order': 1, 'label': '3888.ha.24c', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 35866895
{'center': '1944.a1.a1', 'center_index': 1944, 'center_order': 2, 'counter': 66, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '3888.ha', 'group_counter': 183, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.ha', 'image_order': 3888, 'indicator': 1, 'kernel': '3888.a1.a1', 'kernel_order': 1, 'label': '3888.ha.24d', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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 290 matching records in this table.

id: 204502300
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3888, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '3888.ha.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': '3888.ha', 'subgroup_hash': 2065347936632301655, 'subgroup_order': 3888, 'subgroup_tex': 'D_9^2:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 204502411
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1944, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.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': '1944.2687', 'subgroup_hash': 2687, 'subgroup_order': 1944, 'subgroup_tex': 'D_9^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502513
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1944, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.1221', 'subgroup_hash': 1221, 'subgroup_order': 1944, 'subgroup_tex': 'C_9^2:(C_2\\times C_{12})', 'supersolvable': True, 'sylow': 0}
id: 204502524
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1944, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': '1944.2664', 'subgroup_hash': 2664, 'subgroup_order': 1944, 'subgroup_tex': 'C_2\\times C_9^2:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 204502535
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1296, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.655', 'subgroup_hash': 655, 'subgroup_order': 1296, 'subgroup_tex': 'D_9^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 204502546
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 972, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.660', 'subgroup_hash': 660, 'subgroup_order': 972, 'subgroup_tex': 'C_2\\times C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502557
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 972, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.432', 'subgroup_hash': 432, 'subgroup_order': 972, 'subgroup_tex': 'D_9^2:C_3', 'supersolvable': True, 'sylow': 0}
id: 204502568
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 972, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.432', 'subgroup_hash': 432, 'subgroup_order': 972, 'subgroup_tex': 'D_9^2:C_3', 'supersolvable': True, 'sylow': 0}
id: 204502579
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 486, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '972.611', 'subgroup_hash': 611, 'subgroup_order': 972, 'subgroup_tex': 'C_2\\times C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502301
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 486, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '972.294', 'subgroup_hash': 294, 'subgroup_order': 972, 'subgroup_tex': 'C_9^2:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 204502312
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 486, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '972.432', 'subgroup_hash': 432, 'subgroup_order': 972, 'subgroup_tex': 'D_9^2:C_3', 'supersolvable': True, 'sylow': 0}
id: 204502323
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 486, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '972.409', 'subgroup_hash': 409, 'subgroup_order': 972, 'subgroup_tex': 'C_9^2:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 204502334
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.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': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.296', 'subgroup_hash': 296, 'subgroup_order': 648, 'subgroup_tex': 'D_9\\times D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502345
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.47', 'subgroup_hash': 47, 'subgroup_order': 648, 'subgroup_tex': 'C_{18}.D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502356
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.295', 'subgroup_hash': 295, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_9^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 204502367
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.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': '648.604', 'subgroup_hash': 604, 'subgroup_order': 648, 'subgroup_tex': 'C_{18}:C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 204502378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '648.381', 'subgroup_hash': 381, 'subgroup_order': 648, 'subgroup_tex': 'C_9:(S_3\\times C_{12})', 'supersolvable': True, 'sylow': 0}
id: 204502389
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 486, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.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': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.206', 'subgroup_hash': 206, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502400
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 486, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.159', 'subgroup_hash': 159, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502412
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 486, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.159', 'subgroup_hash': 159, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502423
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 243, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '486.110', 'subgroup_hash': 110, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502434
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 243, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '486.110', 'subgroup_hash': 110, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502445
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, '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': '432.574', 'subgroup_hash': 574, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 204502456
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.74', 'subgroup_hash': 74, 'subgroup_order': 324, 'subgroup_tex': 'C_9:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502467
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.36', 'subgroup_hash': 36, 'subgroup_order': 324, 'subgroup_tex': 'D_9^2', 'supersolvable': True, 'sylow': 0}
id: 204502478
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.36', 'subgroup_hash': 36, 'subgroup_order': 324, 'subgroup_tex': 'D_9^2', 'supersolvable': True, 'sylow': 0}
id: 204502489
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.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': '324.141', 'subgroup_hash': 141, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.C_6^2', 'supersolvable': True, 'sylow': 0}
id: 204502500
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '324.140', 'subgroup_hash': 140, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_6^2', 'supersolvable': True, 'sylow': 0}
id: 204502511
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '324.64', 'subgroup_hash': 64, 'subgroup_order': 324, 'subgroup_tex': 'C_{18}:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502514
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '324.61', 'subgroup_hash': 61, 'subgroup_order': 324, 'subgroup_tex': 'C_9\\times D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502515
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '324.146', 'subgroup_hash': 146, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 204502516
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '324.146', 'subgroup_hash': 146, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 204502517
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '324.95', 'subgroup_hash': 95, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.C_{12}', 'supersolvable': True, 'sylow': 0}
id: 204502518
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '324.94', 'subgroup_hash': 94, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\times C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 204502519
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '324.6', 'subgroup_hash': 6, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_{36}', 'supersolvable': True, 'sylow': 0}
id: 204502520
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.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': '324.9', 'subgroup_hash': 9, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_{36}', 'supersolvable': True, 'sylow': 0}
id: 204502521
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.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': '324.118', 'subgroup_hash': 118, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502522
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.118', 'subgroup_hash': 118, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502523
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.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': '324.118', 'subgroup_hash': 118, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502525
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.118', 'subgroup_hash': 118, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502526
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.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': '324.36', 'subgroup_hash': 36, 'subgroup_order': 324, 'subgroup_tex': 'D_9^2', 'supersolvable': True, 'sylow': 0}
id: 204502527
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.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': '324.35', 'subgroup_hash': 35, 'subgroup_order': 324, 'subgroup_tex': 'C_9^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 204502528
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 243, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '3888.ha.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': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.47', 'subgroup_hash': 47, 'subgroup_order': 243, 'subgroup_tex': 'C_9^2:C_3', 'supersolvable': True, 'sylow': 3}
id: 204502529
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502530
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.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': '216.111', 'subgroup_hash': 111, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502531
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.101', 'subgroup_hash': 101, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502532
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '216.120', 'subgroup_hash': 120, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502533
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 204502534
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '216.53', 'subgroup_hash': 53, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502536
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '216.28', 'subgroup_hash': 28, 'subgroup_order': 216, 'subgroup_tex': 'C_6.D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502537
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 162, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.23', 'subgroup_hash': 23, 'subgroup_order': 162, 'subgroup_tex': 'C_9\\times C_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502538
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 162, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.16', 'subgroup_hash': 16, 'subgroup_order': 162, 'subgroup_tex': 'C_9:D_9', 'supersolvable': True, 'sylow': 0}
id: 204502539
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 162, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.ha.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.16', 'subgroup_hash': 16, 'subgroup_order': 162, 'subgroup_tex': 'C_9:D_9', 'supersolvable': True, 'sylow': 0}
id: 204502540
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502541
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502542
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '162.25', 'subgroup_hash': 25, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '162.25', 'subgroup_hash': 25, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502544
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '162.37', 'subgroup_hash': 37, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
id: 204502545
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.37', 'subgroup_hash': 37, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
id: 204502547
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502548
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502549
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '162.6', 'subgroup_hash': 6, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.6', 'subgroup_hash': 6, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502551
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '162.3', 'subgroup_hash': 3, 'subgroup_order': 162, 'subgroup_tex': 'C_9\\times D_9', 'supersolvable': True, 'sylow': 0}
id: 204502552
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.3', 'subgroup_hash': 3, 'subgroup_order': 162, 'subgroup_tex': 'C_9\\times D_9', 'supersolvable': True, 'sylow': 0}
id: 204502553
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
id: 204502554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
id: 204502555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
id: 204502556
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
id: 204502558
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 204502559
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502560
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 204502561
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502562
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.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': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502563
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502564
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502567
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
id: 204502569
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502570
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502571
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502572
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
id: 204502573
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 204502574
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.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': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
id: 204502575
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.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': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
id: 204502576
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.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': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 204502577
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.r1.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': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 204502578
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.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': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 204502580
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502581
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502582
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
id: 204502583
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502585
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502586
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
id: 204502587
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.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': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
id: 204502588
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
id: 204502589
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.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': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
id: 204502302
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.ha', 'ambient_counter': 183, 'ambient_order': 3888, 'ambient_tex': 'D_9^2:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.ha.36.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', '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 290 matching records in this table.

id: 204502300
{'ambient': '3888.ha', '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': '1944.a1.a1', 'complements': ['3888.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2154, 3781, 8366, 4737, 3757, 5057, 6574, 6244], 'generators': [3, 1296, 1068, 912, 216, 6, 2736, 432, 4], 'label': '3888.ha.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', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1944.2315', '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': '1944.2315'}
id: 204502301
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '648.604', 'aut_weyl_index': 12, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1', '12.l1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1729, -1, 8479, -1, 2289, -1, 8295, -1], 'generators': [1131, 2064, 1296, 4, 1440, 432, 2898], 'label': '3888.ha.4.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.d1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
id: 204502302
{'ambient': '3888.ha', 'aut_centralizer_order': 2, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '324.118', 'aut_weyl_index': 24, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.n1.b1', '18.c1.a1'], 'contains': ['72.l1.b1', '72.o1.b1', '72.bb1.a1', '108.w1.b1', '108.y1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6189, -1, 312, -1, 8718, -1, 1863, -1], 'generators': [1998, 1296, 1068, 1728, 144], 'label': '3888.ha.36.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.y1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.b1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
id: 204502303
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '18.e1.a1'], 'contains': ['72.r1.a1', '108.z1.a1', '324.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3369, -1, 7350, -1, 4030, -1, 6482, -1], 'generators': [3, 1296, 4, 6, 2736], 'label': '3888.ha.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.z1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 204502304
{'ambient': '3888.ha', 'aut_centralizer_order': 324, 'aut_label': '48.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.10', 'aut_weyl_index': 324, 'centralizer': '24.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.k1.a1', '24.k1.b1'], 'contains': ['144.d1.a1', '144.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4457, 6120, 5989, 5535, 4986, 5927, 5862, 6028], 'generators': [912, 432], 'label': '3888.ha.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '3888.ha', 'quotient_action_image': '24.10', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.10'}
id: 204502305
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.38', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.d1.a1', '24.h1.a1', '24.h1.b1', '24.i1.a1', '24.i1.b1', '24.l1.a1', '24.n1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '144.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8715, -1, 4840, -1, 6234, -1, 4516, -1], 'generators': [4, 432, 2736], 'label': '3888.ha.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
id: 204502306
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.38', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.e1.a1', '24.m1.a1', '24.o1.a1'], 'contains': ['144.a1.a1', '144.e1.a1', '144.g1.a1', '144.h1.a1', '144.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4041, -1, 7146, -1, 3453, -1, 7347, -1], 'generators': [4, 912, 1296], 'label': '3888.ha.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': '3888.ha', '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': '108.38'}
id: 204502307
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '54.12', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.f1.a1', '24.j1.a1', '24.j1.b1'], 'contains': ['144.d1.a1', '144.f1.a1', '144.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4830, -1, 5042, -1, 5090, -1, 5009, -1], 'generators': [916, 432], 'label': '3888.ha.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.d1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.12'}
id: 204502308
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '54.12', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.g1.a1'], 'contains': ['144.e1.a1', '144.f1.a1', '144.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3844, -1, 6673, -1, 4108, -1, 7118, -1], 'generators': [436, 912], 'label': '3888.ha.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '48.e1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.12'}
id: 204502309
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '324.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1'], 'contains': ['108.a1.a1', '108.d1.a1', '108.g1.a1', '108.t1.a1', '108.t1.b1', '108.u1.a1', '108.u1.b1', '162.a1.a1', '162.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7211, -1, 3035, -1, 6870, -1, 805, -1], 'generators': [216, 1296, 2502, 1068, 2740], 'label': '3888.ha.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502310
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 54, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.c1.a1', '27.a1.a1'], 'contains': ['108.e1.a1', '108.k1.a1', '108.v1.a1', '108.w1.a1', '108.w1.b1', '162.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4388, -1, 710, -1, 6278, -1, 2181, -1], 'generators': [216, 1296, 918, 1068, 2736], 'label': '3888.ha.54.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '1944.2315', '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': '72.40'}
id: 204502311
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '108.26', 'aut_weyl_index': 72, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.c1.a1'], 'contains': ['108.b1.a1', '108.f1.a1', '108.i1.a1', '108.x1.a1', '108.x1.b1', '108.y1.a1', '108.y1.b1', '162.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7428, -1, 293, -1, 9517, -1, 1712, -1], 'generators': [216, 1296, 2502, 1068, 432], 'label': '3888.ha.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '54.c1.a1', 'projective_image': '1944.2315', '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': '54.6'}
id: 204502312
{'ambient': '3888.ha', 'aut_centralizer_order': 2, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1944.2315', 'aut_weyl_index': 4, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.d1.b1', '12.m1.a1', '12.m1.b1', '12.o1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5651, -1, 2367, -1, 7409, -1, 3417, -1], 'generators': [216, 2736, 1728, 6, 1296, 4, 3648], 'label': '3888.ha.4.e1.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.e1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '972.432'}
id: 204502313
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '324.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.f1.a1'], 'contains': ['108.h1.a1', '108.o1.a1', '108.p1.a1', '162.c1.a1', '162.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [290, -1, 9144, -1, 888, -1, 8522, -1], 'generators': [3117, 2736, 1068, 4, 2898], 'label': '3888.ha.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1.a1', 'old_label': '54.d1.a1', 'projective_image': '1944.2315', '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': '6.1'}
id: 204502314
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 54, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.g1.a1', '27.a1.a1'], 'contains': ['108.k1.a1', '108.n1.a1', '162.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [812, -1, 9966, -1, 1875, -1, 8381, -1], 'generators': [3387, 1296, 1068, 2898, 1440], 'label': '3888.ha.54.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '1944.2315', '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': '72.40'}
id: 204502315
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 54, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '18.e1.a1', '27.a1.a1'], 'contains': ['108.k1.a1', '108.z1.a1', '486.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2246, -1, 8127, -1, 3596, -1, 6765, -1], 'generators': [3, 1296, 2892, 6, 2736], 'label': '3888.ha.54.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.f1.a1', 'projective_image': '1944.2315', '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': '72.40'}
id: 204502316
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '108.26', 'aut_weyl_index': 72, 'centralizer': '972.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.g1.a1'], 'contains': ['108.l1.a1', '108.q1.a1', '108.s1.a1', '162.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1185, -1, 9292, -1, 509, -1, 9386, -1], 'generators': [1947, 2736, 1068, 2898, 912], 'label': '3888.ha.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '54.g1.a1', 'projective_image': '1944.2315', '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': '54.6'}
id: 204502317
{'ambient': '3888.ha', 'aut_centralizer_order': 108, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '36.b1.a1', '36.i1.a1', '36.n1.a1'], 'contains': ['144.a1.a1', '216.a1.a1', '216.b1.a1', '216.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3258, 9132, 6555, 8713, 4257, 9063, 6328, 9120], 'generators': [2898, 4, 2736, 1296], 'label': '3888.ha.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '1944.2315', 'quotient_action_image': '72.40', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 204502318
{'ambient': '3888.ha', 'aut_centralizer_order': 72, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.a1.a1', '36.e1.a1', '36.g1.a1'], 'contains': ['144.b1.a1', '216.b1.a1', '216.c1.a1', '216.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8868, -1, 4409, -1, 8709, -1, 4253, -1], 'generators': [2898, 4, 3024, 1296], 'label': '3888.ha.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.b1.a1', 'projective_image': '1944.2315', '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': '18.3'}
id: 204502319
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.h1.a1'], 'contains': ['144.c1.a1', '216.b1.a1', '216.d1.a1', '216.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8339, -1, 5768, -1, 6545, -1, 5407, -1], 'generators': [2898, 4, 1872, 1296], 'label': '3888.ha.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '72.c1.a1', 'projective_image': '1944.2315', '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': '18.3'}
id: 204502320
{'ambient': '3888.ha', 'aut_centralizer_order': 324, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.d1.a1', '24.f1.a1', '36.c1.a1', '36.f1.a1', '36.l1.a1'], 'contains': ['144.d1.a1', '216.a1.a1', '216.c1.a1', '216.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5102, -1, 5294, -1, 5926, -1, 4877, -1], 'generators': [2898, 432, 2736, 1296], 'label': '3888.ha.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '1944.2315', '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': '12.5'}
id: 204502321
{'ambient': '3888.ha', 'aut_centralizer_order': 324, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.e1.a1', '24.g1.a1', '36.m1.a1', '36.o1.a1', '36.q1.a1'], 'contains': ['144.e1.a1', '216.a1.a1', '216.g1.a1', '216.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1856, -1, 7681, -1, 2463, -1, 8562, -1], 'generators': [2898, 912, 1296, 2736], 'label': '3888.ha.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.e1.a1', 'projective_image': '1944.2315', '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': '12.5'}
id: 204502322
{'ambient': '3888.ha', 'aut_centralizer_order': 108, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.f1.a1', '24.g1.a1', '36.d1.a1'], 'contains': ['144.f1.a1', '216.a1.a1', '216.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6529, -1, 5568, -1, 5731, -1, 5141, -1], 'generators': [2898, 436, 2736, 1296], 'label': '3888.ha.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '72.f1.a1', 'projective_image': '1944.2315', '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': '18.3'}
id: 204502323
{'ambient': '3888.ha', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1944.2315', 'aut_weyl_index': 4, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.b1.a1', '12.p1.a1', '36.z1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3313, -1, 7337, -1, 4164, -1, 6303, -1], 'generators': [3, 2736, 1728, 4, 1296, 6, 3648], 'label': '3888.ha.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.f1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '972.409'}
id: 204502324
{'ambient': '3888.ha', 'aut_centralizer_order': 108, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.a1', '24.g1.a1', '36.p1.a1'], 'contains': ['144.g1.a1', '216.a1.a1', '216.i1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2517, -1, 6864, -1, 3145, -1, 7613, -1], 'generators': [2898, 916, 1296, 2736], 'label': '3888.ha.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '72.g1.a1', 'projective_image': '1944.2315', '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': '18.3'}
id: 204502325
{'ambient': '3888.ha', 'aut_centralizer_order': 72, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '108.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.j1.a1', '36.r1.a1', '36.s1.a1'], 'contains': ['144.h1.a1', '216.f1.a1', '216.g1.a1', '216.i1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1527, -1, 8807, -1, 1165, -1, 8996, -1], 'generators': [2898, 4, 2496, 2736], 'label': '3888.ha.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '72.h1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502326
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.k1.a1'], 'contains': ['144.i1.a1', '216.f1.a1', '216.h1.a1', '216.i1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2142, -1, 8456, -1, 1559, -1, 8823, -1], 'generators': [2898, 4, 3792, 2736], 'label': '3888.ha.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '72.i1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502327
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.a1.a1', '36.v1.a1', '36.w1.a1'], 'contains': ['144.b1.a1', '216.j1.a1', '216.k1.a1', '216.l1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9900, -1, 3521, -1, 9890, -1, 2900, -1], 'generators': [216, 2596, 48, 144], 'label': '3888.ha.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.j1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502328
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '36.a1.a1', '36.v1.b1', '36.w1.b1'], 'contains': ['144.b1.a1', '216.j1.b1', '216.k1.b1', '216.l1.b1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9900, -1, 1911, -1, 9890, -1, 77, -1], 'generators': [1950, 4, 3024, 1296], 'label': '3888.ha.72.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.j1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502329
{'ambient': '3888.ha', 'aut_centralizer_order': 18, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.i1.a1', '36.b1.a1', '36.t1.a1', '36.u1.a1'], 'contains': ['144.a1.a1', '216.j1.a1', '216.m1.a1', '216.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7897, -1, 3771, -1, 7864, -1, 3301, -1], 'generators': [216, 4, 2736, 1296], 'label': '3888.ha.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.k1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 204502330
{'ambient': '3888.ha', 'aut_centralizer_order': 18, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.i1.b1', '36.b1.a1', '36.t1.a1', '36.u1.b1'], 'contains': ['144.a1.a1', '216.j1.b1', '216.m1.b1', '216.n1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7897, -1, 2331, -1, 7864, -1, 636, -1], 'generators': [1950, 4, 1296, 144], 'label': '3888.ha.72.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.k1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 204502331
{'ambient': '3888.ha', 'aut_centralizer_order': 18, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.k1.a1', '36.c1.a1', '36.x1.a1', '36.y1.a1'], 'contains': ['144.d1.a1', '216.k1.a1', '216.n1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6216, -1, 1344, -1, 8890, -1, 3682, -1], 'generators': [216, 1344, 144, 1296], 'label': '3888.ha.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.l1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
id: 204502332
{'ambient': '3888.ha', 'aut_centralizer_order': 18, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.12', 'aut_weyl_index': 216, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.k1.b1', '36.c1.a1', '36.x1.b1', '36.y1.b1'], 'contains': ['144.d1.a1', '216.k1.b1', '216.n1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6216, -1, 1153, -1, 8890, -1, 1661, -1], 'generators': [1950, 432, 1296, 144], 'label': '3888.ha.72.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.l1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.b1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
id: 204502333
{'ambient': '3888.ha', 'aut_centralizer_order': 18, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.j1.a1', '36.d1.a1'], 'contains': ['144.f1.a1', '216.l1.a1', '216.n1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8070, -1, 2831, -1, 8365, -1, 3543, -1], 'generators': [216, 1348, 144, 1296], 'label': '3888.ha.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '72.m1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502334
{'ambient': '3888.ha', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '3888.gz', 'aut_weyl_index': 2, 'centralizer': '1944.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.b1.b1', '12.f1.a1', '12.o1.a1', '18.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4188, 1702, 1462, 1890, 7217, 554, 3843, 4005], 'generators': [216, 2736, 432, 6, 1296, 1068, 912], 'label': '3888.ha.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '1944.2315', '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': '1944.2315'}
id: 204502335
{'ambient': '3888.ha', 'aut_centralizer_order': 18, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.j1.b1', '36.d1.a1'], 'contains': ['144.f1.a1', '216.l1.b1', '216.n1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8070, -1, 1612, -1, 8365, -1, 787, -1], 'generators': [1950, 436, 1296, 144], 'label': '3888.ha.72.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '72.m1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502336
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.e1.a1', '36.v1.b1', '36.w1.a1'], 'contains': ['144.b1.a1', '216.m1.a1', '216.o1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9644, -1, 3649, -1, 9628, -1, 3173, -1], 'generators': [216, 4, 1728, 1296], 'label': '3888.ha.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.n1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502337
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '36.e1.a1', '36.v1.a1', '36.w1.b1'], 'contains': ['144.b1.a1', '216.m1.b1', '216.o1.b1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9644, -1, 2113, -1, 9628, -1, 2280, -1], 'generators': [1950, 4, 192, 144], 'label': '3888.ha.72.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.n1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502338
{'ambient': '3888.ha', 'aut_centralizer_order': 18, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 72, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.j1.a1', '24.k1.a1', '36.f1.a1', '36.x1.b1', '36.y1.a1'], 'contains': ['144.d1.a1', '216.n1.a1', '216.o1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6009, -1, 1478, -1, 8528, -1, 3905, -1], 'generators': [216, 2736, 1728, 1296], 'label': '3888.ha.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.o1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
id: 204502339
{'ambient': '3888.ha', 'aut_centralizer_order': 18, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 72, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.j1.b1', '24.k1.b1', '36.f1.a1', '36.x1.a1', '36.y1.b1'], 'contains': ['144.d1.a1', '216.n1.b1', '216.o1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6009, -1, 548, -1, 8528, -1, 2582, -1], 'generators': [1950, 1296, 192, 144], 'label': '3888.ha.72.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.o1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
id: 204502340
{'ambient': '3888.ha', 'aut_centralizer_order': 8, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.g1.a1', '36.v1.a1', '36.v1.b1'], 'contains': ['144.b1.a1', '216.p1.a1', '216.r1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9366, -1, 4207, -1, 8119, -1, 4119, -1], 'generators': [6, 4, 432, 1296], 'label': '3888.ha.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.p1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502341
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.h1.a1'], 'contains': ['144.c1.a1', '216.p1.a1', '216.s1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8581, -1, 5092, -1, 5417, -1, 5541, -1], 'generators': [6, 4, 3168, 1296], 'label': '3888.ha.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.a1', 'old_label': '72.q1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502342
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.m1.a1', '36.i1.a1', '36.t1.a1', '36.z1.a1'], 'contains': ['144.a1.a1', '216.p1.a1', '216.q1.a1', '216.t1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3939, -1, 6283, -1, 4451, -1, 6161, -1], 'generators': [6, 4, 2736, 1296], 'label': '3888.ha.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.r1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 204502343
{'ambient': '3888.ha', 'aut_centralizer_order': 8, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.j1.a1'], 'contains': ['144.h1.a1', '216.q1.a1', '216.u1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2712, -1, 8107, -1, 1821, -1, 8262, -1], 'generators': [2502, 4, 912, 2736], 'label': '3888.ha.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.s1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502344
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.k1.a1'], 'contains': ['144.i1.a1', '216.q1.a1', '216.v1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2867, -1, 7936, -1, 2310, -1, 8074, -1], 'generators': [2502, 4, 2208, 2736], 'label': '3888.ha.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.a1', 'old_label': '72.t1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502345
{'ambient': '3888.ha', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '3888.gz', 'aut_weyl_index': 2, 'centralizer': '1944.a1.a1', 'complements': ['648.e1.a1', '648.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.k1.a1', '18.g1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1988, 5357, 8668, 6166, 2948, 4034, 7515, 5560], 'generators': [1131, 1440, 1728, 1068, 1296, 2898, 2064], 'label': '3888.ha.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '1944.2315', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2315'}
id: 204502346
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '324.118', 'aut_weyl_index': 24, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.l1.a1', '36.l1.a1', '36.x1.a1', '36.x1.b1'], 'contains': ['144.d1.a1', '216.r1.a1', '216.s1.a1', '216.t1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5343, -1, 4927, -1, 5200, -1, 4745, -1], 'generators': [6, 1728, 2736, 1296], 'label': '3888.ha.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.u1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
id: 204502347
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '324.118', 'aut_weyl_index': 24, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.m1.a1', '36.m1.a1'], 'contains': ['144.e1.a1', '216.t1.a1', '216.u1.a1', '216.v1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3631, -1, 7808, -1, 3298, -1, 7481, -1], 'generators': [918, 3648, 1296, 2736], 'label': '3888.ha.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '72.v1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
id: 204502348
{'ambient': '3888.ha', 'aut_centralizer_order': 8, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.g1.a1', '36.w1.a1', '36.w1.b1'], 'contains': ['144.b1.a1', '216.w1.a1', '216.y1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9483, -1, 4115, -1, 8229, -1, 4024, -1], 'generators': [1068, 2740, 432, 1296], 'label': '3888.ha.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.w1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502349
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.h1.a1'], 'contains': ['144.c1.a1', '216.w1.a1', '216.z1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9022, -1, 4611, -1, 6390, -1, 5273, -1], 'generators': [1068, 2740, 3168, 1296], 'label': '3888.ha.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.a1', 'old_label': '72.x1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502350
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.o1.a1', '36.i1.a1', '36.u1.a1', '36.u1.b1'], 'contains': ['144.a1.a1', '216.w1.a1', '216.x1.a1', '216.ba1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5496, -1, 5932, -1, 4649, -1, 5990, -1], 'generators': [1068, 4, 2736, 1296], 'label': '3888.ha.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.y1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 204502351
{'ambient': '3888.ha', 'aut_centralizer_order': 8, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.j1.a1'], 'contains': ['144.h1.a1', '216.x1.a1', '216.bb1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3110, -1, 7322, -1, 2038, -1, 7979, -1], 'generators': [1068, 4, 912, 2736], 'label': '3888.ha.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.z1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502352
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.k1.a1'], 'contains': ['144.i1.a1', '216.x1.a1', '216.bc1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3739, -1, 7193, -1, 2616, -1, 7745, -1], 'generators': [1068, 4, 2208, 2736], 'label': '3888.ha.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.a1', 'old_label': '72.ba1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502353
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '324.118', 'aut_weyl_index': 24, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.n1.a1', '36.l1.a1', '36.y1.a1', '36.y1.b1'], 'contains': ['144.d1.a1', '216.y1.a1', '216.z1.a1', '216.ba1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5738, -1, 4703, -1, 6079, -1, 4650, -1], 'generators': [1068, 1728, 2736, 1296], 'label': '3888.ha.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.bb1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
id: 204502354
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '324.118', 'aut_weyl_index': 24, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.o1.a1', '36.m1.a1'], 'contains': ['144.e1.a1', '216.ba1.a1', '216.bb1.a1', '216.bc1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4137, -1, 7028, -1, 3609, -1, 7213, -1], 'generators': [1068, 3648, 1296, 2736], 'label': '3888.ha.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '72.bc1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
id: 204502355
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.14', 'aut_weyl_index': 486, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['162.a1.a1', '162.c1.a1', '162.d1.a1', '243.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [100, -1, 8931, -1, 2654, -1, 6964, -1], 'generators': [2163, 1068, 216, 2740, 2502], 'label': '3888.ha.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': '1944.2315', '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': '4.2'}
id: 204502356
{'ambient': '3888.ha', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '3888.gz', 'aut_weyl_index': 2, 'centralizer': '1944.a1.a1', 'complements': ['648.e1.a1', '648.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.p1.a1', '54.f1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2223, 3369, 7671, 4242, 3942, 2141, 6529, 9157], 'generators': [3, 2736, 432, 1068, 1296, 6, 912], 'label': '3888.ha.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '1944.2315', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2315'}
id: 204502357
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '54.a1.a1'], 'contains': ['216.b1.a1', '216.j1.a1', '216.j1.b1', '324.a1.a1', '324.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7757, -1, 3109, -1, 7559, -1, 345, -1], 'generators': [216, 2898, 2596, 144], 'label': '3888.ha.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.a1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502358
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.c1.a1', '54.c1.a1'], 'contains': ['216.c1.a1', '216.k1.a1', '216.k1.b1', '324.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7395, -1, 1340, -1, 9369, -1, 1171, -1], 'generators': [216, 2898, 48, 144], 'label': '3888.ha.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.b1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 204502359
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.d1.a1'], 'contains': ['216.e1.a1', '216.l1.a1', '216.l1.b1', '324.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9050, -1, 2246, -1, 9068, -1, 471, -1], 'generators': [216, 2898, 2644, 144], 'label': '3888.ha.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '1944.2315', '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': '3.1'}
id: 204502360
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.e1.a1', '54.a1.a1'], 'contains': ['216.b1.a1', '216.m1.a1', '216.m1.b1', '324.b1.a1', '324.c1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6827, -1, 3217, -1, 7429, -1, 1940, -1], 'generators': [216, 2898, 4, 1296], 'label': '3888.ha.108.d1.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': '108.d1.a1', 'projective_image': '1944.2315', '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': '6.1'}
id: 204502361
{'ambient': '3888.ha', 'aut_centralizer_order': 54, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.a1', '36.d1.a1', '36.f1.a1', '54.b1.a1'], 'contains': ['216.a1.a1', '216.n1.a1', '216.n1.b1', '324.a1.a1', '324.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4915, -1, 1117, -1, 7689, -1, 2079, -1], 'generators': [216, 2898, 2736, 1296], 'label': '3888.ha.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '108.e1.a1', 'projective_image': '1944.2315', '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: 204502362
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 72, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.f1.a1', '54.c1.a1'], 'contains': ['216.c1.a1', '216.o1.a1', '216.o1.b1', '324.c1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7220, -1, 34, -1, 9218, -1, 2465, -1], 'generators': [216, 2898, 1728, 1296], 'label': '3888.ha.108.f1.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': '108.f1.a1', 'projective_image': '1944.2315', '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': '54.6'}
id: 204502363
{'ambient': '3888.ha', 'aut_centralizer_order': 24, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '324.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.h1.a1', '36.i1.a1', '54.a1.a1'], 'contains': ['216.b1.a1', '216.p1.a1', '216.w1.a1', '324.d1.a1', '324.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8423, -1, 6135, -1, 5553, -1, 5658, -1], 'generators': [2502, 1068, 2740, 1296], 'label': '3888.ha.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.g1.a1', 'projective_image': '1944.2315', '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': '6.1'}
id: 204502364
{'ambient': '3888.ha', 'aut_centralizer_order': 24, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '324.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.j1.a1', '36.k1.a1', '54.d1.a1'], 'contains': ['216.f1.a1', '216.q1.a1', '216.x1.a1', '324.d1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2105, -1, 8327, -1, 2174, -1, 7862, -1], 'generators': [2898, 1068, 4, 2736], 'label': '3888.ha.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1.a1', 'old_label': '108.h1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502365
{'ambient': '3888.ha', 'aut_centralizer_order': 8, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.l1.a1', '54.c1.a1'], 'contains': ['216.c1.a1', '216.r1.a1', '216.y1.a1', '324.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7051, -1, 4099, -1, 8011, -1, 4385, -1], 'generators': [2502, 1068, 432, 1296], 'label': '3888.ha.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.i1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502366
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.l1.a1'], 'contains': ['216.d1.a1', '216.s1.a1', '216.z1.a1', '324.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6469, -1, 5574, -1, 5309, -1, 5773, -1], 'generators': [2502, 1068, 3168, 1296], 'label': '3888.ha.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1.a1', 'old_label': '108.j1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502367
{'ambient': '3888.ha', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '648.604', 'aut_weyl_index': 12, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.c1.a1', '12.d1.a1', '12.g1.a1', '12.m1.a1', '12.m1.b1', '12.n1.a1', '12.n1.b1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5894, -1, 2897, -1, 8023, -1, 2610, -1], 'generators': [216, 2736, 1728, 918, 1296, 1068, 4], 'label': '3888.ha.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '6.d1.a1', 'projective_image': '1944.2315', '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': '324.118'}
id: 204502368
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.l1.a1', '36.m1.a1', '54.b1.a1', '54.e1.a1', '54.f1.a1'], 'contains': ['216.a1.a1', '216.t1.a1', '216.ba1.a1', '324.e1.a1', '324.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2794, -1, 6508, -1, 3954, -1, 6495, -1], 'generators': [918, 1068, 2736, 1296], 'label': '3888.ha.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.k1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 204502369
{'ambient': '3888.ha', 'aut_centralizer_order': 8, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '36.m1.a1', '54.g1.a1'], 'contains': ['216.g1.a1', '216.u1.a1', '216.bb1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1675, -1, 8625, -1, 1712, -1, 8691, -1], 'generators': [2898, 1068, 912, 2736], 'label': '3888.ha.108.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '108.l1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502370
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '36.m1.a1'], 'contains': ['216.h1.a1', '216.v1.a1', '216.bc1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2329, -1, 8103, -1, 1929, -1, 8168, -1], 'generators': [2898, 1068, 2208, 2736], 'label': '3888.ha.108.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.a1', 'old_label': '108.m1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502371
{'ambient': '3888.ha', 'aut_centralizer_order': 54, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1.a1', '36.o1.a1', '36.p1.a1', '36.q1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '324.g1.a1', '324.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [942, -1, 9829, -1, 965, -1, 9306, -1], 'generators': [1131, 1296, 2898, 1440], 'label': '3888.ha.108.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '108.n1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 204502372
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1.a1', '36.r1.a1', '54.d1.a1'], 'contains': ['216.f1.a1', '324.g1.a1', '324.i1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [267, -1, 9418, -1, 502, -1, 9648, -1], 'generators': [1131, 2596, 2736, 2898], 'label': '3888.ha.108.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '108.o1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502373
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '108.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1.a1', '36.s1.a1', '54.d1.a1'], 'contains': ['216.f1.a1', '324.h1.a1', '324.i1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [597, -1, 9254, -1, 199, -1, 9478, -1], 'generators': [1131, 4, 2898, 1440], 'label': '3888.ha.108.p1.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.p1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502374
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '108.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1.a1', '36.r1.a1', '54.g1.a1'], 'contains': ['216.g1.a1', '324.g1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1137, -1, 9665, -1, 351, -1, 9964, -1], 'generators': [1131, 2496, 2898, 2736], 'label': '3888.ha.108.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '108.q1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 204502375
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1296, 'centralizer': '108.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '36.r1.a1'], 'contains': ['216.i1.a1', '324.g1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [793, -1, 9541, -1, 813, -1, 9873, -1], 'generators': [1131, 2356, 2898, 2736], 'label': '3888.ha.108.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '108.r1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 204502376
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 72, 'centralizer': '108.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.a1', '36.s1.a1', '54.g1.a1'], 'contains': ['216.g1.a1', '324.h1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1244, -1, 9090, -1, 44, -1, 9780, -1], 'generators': [1131, 2898, 3072, 1440], 'label': '3888.ha.108.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '108.s1.a1', 'projective_image': '1944.2315', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502377
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '324.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.v1.a1', '54.a1.a1'], 'contains': ['216.j1.a1', '216.m1.b1', '216.p1.a1', '324.j1.a1', '324.l1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7886, -1, 2613, -1, 7106, -1, 1801, -1], 'generators': [1944, 6, 4, 144], 'label': '3888.ha.108.t1.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.t1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502378
{'ambient': '3888.ha', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '648.604', 'aut_weyl_index': 12, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.h1.a1', '12.i1.a1', '12.j1.a1', '18.d1.a1', '18.f1.a1', '18.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1263, -1, 8950, -1, 1768, -1, 8577, -1], 'generators': [669, 1296, 3648, 1068, 2736, 4, 2898], 'label': '3888.ha.6.e1.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': '6.e1.a1', 'projective_image': '1944.2315', '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': '324.118'}
id: 204502379
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '324.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.v1.b1', '54.a1.a1'], 'contains': ['216.j1.b1', '216.m1.a1', '216.p1.a1', '324.j1.a1', '324.l1.b1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7886, -1, 2746, -1, 7106, -1, 926, -1], 'generators': [648, 6, 4, 1296], 'label': '3888.ha.108.t1.b1', '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.t1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502380
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '324.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '36.w1.a1', '54.a1.a1'], 'contains': ['216.j1.a1', '216.m1.a1', '216.w1.a1', '324.k1.a1', '324.m1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8257, -1, 3651, -1, 7268, -1, 3055, -1], 'generators': [216, 1068, 2740, 1296], 'label': '3888.ha.108.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.u1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502381
{'ambient': '3888.ha', 'aut_centralizer_order': 12, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '324.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.b1', '36.w1.b1', '54.a1.a1'], 'contains': ['216.j1.b1', '216.m1.b1', '216.w1.a1', '324.k1.b1', '324.m1.b1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8257, -1, 2469, -1, 7268, -1, 232, -1], 'generators': [1854, 1068, 2740, 1296], 'label': '3888.ha.108.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.u1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 204502382
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.x1.a1', '36.x1.b1', '54.b1.a1'], 'contains': ['216.n1.a1', '216.n1.b1', '216.t1.a1', '324.l1.a1', '324.l1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5629, -1, 793, -1, 6693, -1, 2190, -1], 'generators': [648, 6, 2736, 1296], 'label': '3888.ha.108.v1.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.v1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 204502383
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '36.y1.a1', '54.b1.a1'], 'contains': ['216.n1.a1', '216.ba1.a1', '324.m1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5905, -1, 2929, -1, 6790, -1, 3793, -1], 'generators': [216, 1068, 2736, 1296], 'label': '3888.ha.108.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.w1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 204502384
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.b1', '36.y1.b1', '54.b1.a1'], 'contains': ['216.n1.b1', '216.ba1.a1', '324.m1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5905, -1, 606, -1, 6790, -1, 1297, -1], 'generators': [1998, 1068, 144, 1296], 'label': '3888.ha.108.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.w1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 204502385
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1.a1', '36.x1.a1', '54.c1.a1'], 'contains': ['216.k1.a1', '216.o1.b1', '216.r1.a1', '324.l1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7610, -1, 123, -1, 9519, -1, 2373, -1], 'generators': [1944, 6, 192, 144], 'label': '3888.ha.108.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.x1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502386
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1.b1', '36.x1.b1', '54.c1.a1'], 'contains': ['216.k1.b1', '216.o1.a1', '216.r1.a1', '324.l1.b1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7610, -1, 969, -1, 9519, -1, 1546, -1], 'generators': [216, 6, 3024, 1296], 'label': '3888.ha.108.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.x1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502387
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1.a1', '36.y1.a1', '54.c1.a1'], 'contains': ['216.k1.a1', '216.o1.a1', '216.y1.a1', '324.m1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8018, -1, 1971, -1, 9737, -1, 3427, -1], 'generators': [216, 1068, 432, 1296], 'label': '3888.ha.108.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.y1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502388
{'ambient': '3888.ha', 'aut_centralizer_order': 4, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 144, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1.b1', '36.y1.b1', '54.c1.a1'], 'contains': ['216.k1.b1', '216.o1.b1', '216.y1.a1', '324.m1.b1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8018, -1, 210, -1, 9737, -1, 1041, -1], 'generators': [1854, 1068, 432, 1296], 'label': '3888.ha.108.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.y1.b1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
id: 204502389
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '216.157', 'aut_weyl_index': 36, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4261, 9162, 6050, 9189, 4361, 9091, 5973, 8473], 'generators': [2898, 1296, 2736, 4, 912, 432], 'label': '3888.ha.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', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '1944.2315', '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': '216.157'}
id: 204502390
{'ambient': '3888.ha', 'aut_centralizer_order': 6, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '648.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '36.z1.a1', '54.f1.a1'], 'contains': ['216.t1.a1', '972.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3459, -1, 7662, -1, 3782, -1, 6682, -1], 'generators': [3, 6, 2736, 1296], 'label': '3888.ha.108.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.z1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 204502391
{'ambient': '3888.ha', 'aut_centralizer_order': 108, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.c1.a1', '72.a1.a1', '72.k1.a1', '72.k1.b1', '72.r1.a1', '72.y1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4755, 8148, 5802, 7760, 4649, 8011, 5491, 6796], 'generators': [4, 2736, 1296], 'label': '3888.ha.144.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['16.a1.a1', '72.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '3888.ha', 'quotient_action_image': '72.40', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 204502392
{'ambient': '3888.ha', 'aut_centralizer_order': 72, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.b1.a1', '72.j1.a1', '72.j1.b1', '72.n1.a1', '72.n1.b1', '72.p1.a1', '72.w1.a1'], 'contains': ['432.b1.a1', '432.c1.a1', '432.e1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9707, -1, 4115, -1, 8221, -1, 3963, -1], 'generators': [4, 432], 'label': '3888.ha.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.b1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502393
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.c1.a1', '72.q1.a1', '72.x1.a1'], 'contains': ['432.b1.a1', '432.d1.a1', '432.e1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9317, -1, 4533, -1, 6553, -1, 4808, -1], 'generators': [4, 3168], 'label': '3888.ha.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '144.c1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502394
{'ambient': '3888.ha', 'aut_centralizer_order': 324, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.d1.a1', '72.d1.a1', '72.l1.a1', '72.l1.b1', '72.o1.a1', '72.o1.b1', '72.u1.a1', '72.bb1.a1'], 'contains': ['432.a1.a1', '432.c1.a1', '432.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5246, -1, 4796, -1, 5901, -1, 4320, -1], 'generators': [432, 2736], 'label': '3888.ha.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
id: 204502395
{'ambient': '3888.ha', 'aut_centralizer_order': 324, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 648, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.c1.a1', '48.e1.a1', '72.e1.a1', '72.v1.a1', '72.bc1.a1'], 'contains': ['432.a1.a1', '432.g1.a1', '432.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4196, -1, 7235, -1, 3553, -1, 7347, -1], 'generators': [912, 1296], 'label': '3888.ha.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.e1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
id: 204502396
{'ambient': '3888.ha', 'aut_centralizer_order': 108, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.d1.a1', '48.e1.a1', '72.f1.a1', '72.m1.a1', '72.m1.b1'], 'contains': ['432.a1.a1', '432.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6037, -1, 5162, -1, 5739, -1, 4550, -1], 'generators': [436, 2736], 'label': '3888.ha.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '144.f1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502397
{'ambient': '3888.ha', 'aut_centralizer_order': 108, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '72.g1.a1'], 'contains': ['432.a1.a1', '432.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4357, -1, 6710, -1, 3820, -1, 7162, -1], 'generators': [916, 1296], 'label': '3888.ha.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '144.g1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502398
{'ambient': '3888.ha', 'aut_centralizer_order': 72, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '108.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '72.h1.a1', '72.s1.a1', '72.z1.a1'], 'contains': ['432.f1.a1', '432.g1.a1', '432.i1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3109, -1, 7557, -1, 2039, -1, 8177, -1], 'generators': [4, 2496], 'label': '3888.ha.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '144.h1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 204502399
{'ambient': '3888.ha', 'aut_centralizer_order': 36, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '18.3', 'aut_weyl_index': 432, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '72.i1.a1', '72.t1.a1', '72.ba1.a1'], 'contains': ['432.f1.a1', '432.h1.a1', '432.i1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3612, -1, 7466, -1, 2407, -1, 7934, -1], 'generators': [4, 3792], 'label': '3888.ha.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '144.i1.a1', 'projective_image': '3888.ha', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}

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.