LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-06-13T07:47:41.411201

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [2, 3, 4, 4, 3, 2, 6, 4, 4, 12], 'aut_gens': [[1, 2, 24, 72, 216, 648], [1369, 1154, 24, 1440, 432, 648], [1009, 218, 24, 72, 864, 648], [805, 1598, 24, 1008, 288, 648], [1225, 806, 24, 1080, 1368, 648], [433, 146, 24, 720, 864, 648], [1254, 141, 16, 72, 1224, 1296], [449, 146, 24, 144, 432, 648], [449, 1294, 48, 432, 720, 648], [589, 566, 48, 504, 576, 648], [433, 1286, 24, 432, 720, 648]], 'aut_group': '5184.qp', 'aut_hash': 4988806636622200354, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5184, 'aut_permdeg': 108, 'aut_perms': [2328978836847764210971886107659943228777781189998085463598889518949266077694402671114513621511740820763628962925574331662193745258646782784803012329117304736812251023513773, 1204434711613190891401774632263508773292994489752359271138845875186077979509341633531938671516863168397574479686156332258015169543797785728233475764883297074270869297540601946, 277299609501240848393810460825874888695548289999832054978061197703132435957696802299145057852008452074136994776987466598818497351918655412902533246872113361688133455528489397, 6863465567810317002349451831567753874058727030440651238251845341320964727333307196276925185946191810402854239682235288868558380366147169842712321614145623613945327398912013, 709202901038470721369768072666572140345235878798197971747769090927701060107965198264989407220290096979356397959252172455369725640324757484234125117173893158307133063546881653, 817102056963850716477864179250024446048367906592432919949700650804989983431556195488982518530634379423040873233733309723293327657488087466726163313905144050805127083382667149, 378599834654834241483605539074647237167625672118334455221116369595547338068590947564059005866148398312318865987378254403260145701571899945973187166997875195348841089741402791, 1187409709507465493380168821591343082174096019228210683553454443255671135696157525975386003916980661968511571849527183641144909822398382089846694110774424922755975717055693685, 718197270786657029916585327772923894968227457552069608633244174723312190897023429517654561287783183058143181391563065092987438384331573050703533139332895436325349536149111508, 387100626883582696368515050789655451914169925555992880072685540386628141974310323256238126043095185430243692715953684766127175320524903462033632629688577625743995886833478367], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 1, 2, 1], [3, 2, 2, 3], [3, 4, 1, 1], [3, 4, 2, 1], [3, 24, 1, 1], [3, 24, 4, 2], [4, 54, 2, 1], [4, 162, 1, 1], [6, 9, 2, 1], [6, 18, 2, 3], [6, 36, 1, 1], [6, 36, 2, 1], [12, 54, 2, 2], [12, 54, 4, 3], [12, 162, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_3^2\\times S_3^2):\\SD_{16}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '5184.qp', 'autcentquo_hash': 4988806636622200354, 'autcentquo_nilpotent': False, 'autcentquo_order': 5184, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '(C_3^2\\times S_3^2):\\SD_{16}', 'cc_stats': [[1, 1, 1], [2, 9, 1], [3, 1, 2], [3, 2, 6], [3, 4, 3], [3, 24, 9], [4, 54, 2], [4, 162, 1], [6, 9, 2], [6, 18, 6], [6, 36, 3], [12, 54, 16], [12, 162, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': '648.729', 'commutator_count': 2, 'commutator_label': '486.230', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3557, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [3, 24, 1, 1], [3, 24, 2, 4], [4, 54, 1, 2], [4, 162, 1, 1], [6, 9, 2, 1], [6, 18, 1, 2], [6, 18, 2, 2], [6, 36, 1, 1], [6, 36, 2, 1], [12, 54, 2, 4], [12, 54, 4, 2], [12, 162, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 108, 'exponent': 12, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '648.729', 'hash': 3557, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 12, 3, 3, 3, 1], 'inner_gens': [[1, 22, 24, 216, 792, 648], [5, 2, 48, 1584, 1152, 648], [1, 50, 24, 72, 216, 648], [1153, 1082, 24, 72, 1512, 648], [1585, 578, 24, 720, 216, 648], [1, 2, 24, 72, 216, 648]], 'inner_hash': 729, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': True, 'inner_tex': 'C_3^4:Q_8', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 9], [3, 8], [4, 2], [6, 18], [8, 9], [12, 4]], 'label': '1944.3557', 'linC_count': 144, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 24, 'linQ_dim': 10, 'linQ_dim_count': 20, 'linR_count': 20, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C3^2:SU(3,2)', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 54, 'number_divisions': 31, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 107, 'number_subgroup_classes': 191, 'number_subgroups': 2646, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 9], [3, 242], [4, 270], [6, 234], [12, 1188]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 10, 24, 72, 216, 648], [6, 61, 8, 1368, 576, 1296]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [6, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 4], [6, 4], [8, 1], [12, 5], [16, 4], [24, 4]], 'representations': {'PC': {'code': 99728284078434939821445511717423707898136789516692457247, 'gens': [1, 2, 5, 6, 7, 8], 'pres': [8, -2, -2, -2, -3, -3, -3, 3, -3, 96, 353, 41, 482, 66, 515, 972, 10373, 38029, 9525, 44358, 32270, 15142, 1222]}, 'Perm': {'d': 33, 'gens': [26278700897064253163352636225467656, 34769199552829649749273314409959743, 43257700129935055708975096767219840, 306689418256830869593958689182101760, 578340372045468302302441993787750400, 325, 435, 849970019550760644988159745280445440]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:\\SU(3,2)', '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: 137000594
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 3557, 'group_order': 1944, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 137000605
{'aut_label': '2A', 'centralizer': '9.a1.a1', 'counter': 2, 'group_counter': 3557, 'group_order': 1944, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 12, 'size': 9}
id: 137000616
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 3557, 'group_order': 1944, 'label': '3A1', 'order': 3, 'powers': [4, 1], 'representative': 648, 'size': 1}
id: 137000627
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 3557, 'group_order': 1944, 'label': '3A-1', 'order': 3, 'powers': [3, 1], 'representative': 1296, 'size': 1}
id: 137000638
{'aut_label': '3B', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 3557, 'group_order': 1944, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 24, 'size': 2}
id: 137000644
{'aut_label': '3B', 'centralizer': '2.a1.b1', 'counter': 6, 'group_counter': 3557, 'group_order': 1944, 'label': '3C', 'order': 3, 'powers': [6, 1], 'representative': 16, 'size': 2}
id: 137000645
{'aut_label': '3D1', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 3557, 'group_order': 1944, 'label': '3D1', 'order': 3, 'powers': [8, 1], 'representative': 1320, 'size': 2}
id: 137000646
{'aut_label': '3D-1', 'centralizer': '2.a1.a1', 'counter': 8, 'group_counter': 3557, 'group_order': 1944, 'label': '3D-1', 'order': 3, 'powers': [7, 1], 'representative': 696, 'size': 2}
id: 137000647
{'aut_label': '3D1', 'centralizer': '2.a1.b1', 'counter': 9, 'group_counter': 3557, 'group_order': 1944, 'label': '3E1', 'order': 3, 'powers': [10, 1], 'representative': 656, 'size': 2}
id: 137000595
{'aut_label': '3D-1', 'centralizer': '2.a1.b1', 'counter': 10, 'group_counter': 3557, 'group_order': 1944, 'label': '3E-1', 'order': 3, 'powers': [9, 1], 'representative': 1312, 'size': 2}
id: 137000596
{'aut_label': '3F', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 3557, 'group_order': 1944, 'label': '3F', 'order': 3, 'powers': [11, 1], 'representative': 56, 'size': 4}
id: 137000597
{'aut_label': '3G1', 'centralizer': '4.a1.a1', 'counter': 12, 'group_counter': 3557, 'group_order': 1944, 'label': '3G1', 'order': 3, 'powers': [13, 1], 'representative': 1352, 'size': 4}
id: 137000598
{'aut_label': '3G1', 'centralizer': '4.a1.a1', 'counter': 13, 'group_counter': 3557, 'group_order': 1944, 'label': '3G-1', 'order': 3, 'powers': [12, 1], 'representative': 688, 'size': 4}
id: 137000599
{'aut_label': '3H', 'centralizer': '24.c1.a1', 'counter': 14, 'group_counter': 3557, 'group_order': 1944, 'label': '3H', 'order': 3, 'powers': [14, 1], 'representative': 216, 'size': 24}
id: 137000600
{'aut_label': '3I1', 'centralizer': '24.c1.a1', 'counter': 15, 'group_counter': 3557, 'group_order': 1944, 'label': '3I1', 'order': 3, 'powers': [16, 1], 'representative': 240, 'size': 24}
id: 137000601
{'aut_label': '3I1', 'centralizer': '24.c1.a1', 'counter': 16, 'group_counter': 3557, 'group_order': 1944, 'label': '3I-1', 'order': 3, 'powers': [15, 1], 'representative': 264, 'size': 24}
id: 137000602
{'aut_label': '3I1', 'centralizer': '24.c1.a1', 'counter': 17, 'group_counter': 3557, 'group_order': 1944, 'label': '3J1', 'order': 3, 'powers': [18, 1], 'representative': 224, 'size': 24}
id: 137000603
{'aut_label': '3I1', 'centralizer': '24.c1.a1', 'counter': 18, 'group_counter': 3557, 'group_order': 1944, 'label': '3J-1', 'order': 3, 'powers': [17, 1], 'representative': 80, 'size': 24}
id: 137000604
{'aut_label': '3K1', 'centralizer': '24.c1.a1', 'counter': 19, 'group_counter': 3557, 'group_order': 1944, 'label': '3K1', 'order': 3, 'powers': [20, 1], 'representative': 248, 'size': 24}
id: 137000606
{'aut_label': '3K1', 'centralizer': '24.c1.a1', 'counter': 20, 'group_counter': 3557, 'group_order': 1944, 'label': '3K-1', 'order': 3, 'powers': [19, 1], 'representative': 128, 'size': 24}
id: 137000607
{'aut_label': '3K1', 'centralizer': '24.c1.a1', 'counter': 21, 'group_counter': 3557, 'group_order': 1944, 'label': '3L1', 'order': 3, 'powers': [22, 1], 'representative': 104, 'size': 24}
id: 137000608
{'aut_label': '3K1', 'centralizer': '24.c1.a1', 'counter': 22, 'group_counter': 3557, 'group_order': 1944, 'label': '3L-1', 'order': 3, 'powers': [21, 1], 'representative': 272, 'size': 24}
id: 137000609
{'aut_label': '4A', 'centralizer': '54.a1.a1', 'counter': 23, 'group_counter': 3557, 'group_order': 1944, 'label': '4A', 'order': 4, 'powers': [2, 23], 'representative': 13, 'size': 54}
id: 137000610
{'aut_label': '4A', 'centralizer': '54.a1.b1', 'counter': 24, 'group_counter': 3557, 'group_order': 1944, 'label': '4B', 'order': 4, 'powers': [2, 24], 'representative': 1002, 'size': 54}
id: 137000611
{'aut_label': '4C', 'centralizer': '162.b1.a1', 'counter': 25, 'group_counter': 3557, 'group_order': 1944, 'label': '4C', 'order': 4, 'powers': [2, 25], 'representative': 431, 'size': 162}
id: 137000612
{'aut_label': '6A1', 'centralizer': '9.a1.a1', 'counter': 26, 'group_counter': 3557, 'group_order': 1944, 'label': '6A1', 'order': 6, 'powers': [3, 2], 'representative': 228, 'size': 9}
id: 137000613
{'aut_label': '6A1', 'centralizer': '9.a1.a1', 'counter': 27, 'group_counter': 3557, 'group_order': 1944, 'label': '6A-1', 'order': 6, 'powers': [4, 2], 'representative': 1524, 'size': 9}
id: 137000614
{'aut_label': '6B', 'centralizer': '18.a1.a1', 'counter': 28, 'group_counter': 3557, 'group_order': 1944, 'label': '6B', 'order': 6, 'powers': [5, 2], 'representative': 60, 'size': 18}
id: 137000615
{'aut_label': '6B', 'centralizer': '18.a1.b1', 'counter': 29, 'group_counter': 3557, 'group_order': 1944, 'label': '6C', 'order': 6, 'powers': [6, 2], 'representative': 308, 'size': 18}
id: 137000617
{'aut_label': '6D1', 'centralizer': '18.a1.a1', 'counter': 30, 'group_counter': 3557, 'group_order': 1944, 'label': '6D1', 'order': 6, 'powers': [7, 2], 'representative': 708, 'size': 18}
id: 137000618
{'aut_label': '6D-1', 'centralizer': '18.a1.a1', 'counter': 31, 'group_counter': 3557, 'group_order': 1944, 'label': '6D-1', 'order': 6, 'powers': [8, 2], 'representative': 1332, 'size': 18}
id: 137000619
{'aut_label': '6D1', 'centralizer': '18.a1.b1', 'counter': 32, 'group_counter': 3557, 'group_order': 1944, 'label': '6E1', 'order': 6, 'powers': [9, 2], 'representative': 1156, 'size': 18}
id: 137000620
{'aut_label': '6D-1', 'centralizer': '18.a1.b1', 'counter': 33, 'group_counter': 3557, 'group_order': 1944, 'label': '6E-1', 'order': 6, 'powers': [10, 2], 'representative': 524, 'size': 18}
id: 137000621
{'aut_label': '6F', 'centralizer': '36.b1.a1', 'counter': 34, 'group_counter': 3557, 'group_order': 1944, 'label': '6F', 'order': 6, 'powers': [11, 2], 'representative': 28, 'size': 36}
id: 137000622
{'aut_label': '6G1', 'centralizer': '36.b1.a1', 'counter': 35, 'group_counter': 3557, 'group_order': 1944, 'label': '6G1', 'order': 6, 'powers': [12, 2], 'representative': 676, 'size': 36}
id: 137000623
{'aut_label': '6G1', 'centralizer': '36.b1.a1', 'counter': 36, 'group_counter': 3557, 'group_order': 1944, 'label': '6G-1', 'order': 6, 'powers': [13, 2], 'representative': 244, 'size': 36}
id: 137000624
{'aut_label': '12A1', 'centralizer': '54.a1.a1', 'counter': 37, 'group_counter': 3557, 'group_order': 1944, 'label': '12A1', 'order': 12, 'powers': [28, 23], 'representative': 25, 'size': 54}
id: 137000625
{'aut_label': '12A1', 'centralizer': '54.a1.a1', 'counter': 38, 'group_counter': 3557, 'group_order': 1944, 'label': '12A5', 'order': 12, 'powers': [28, 23], 'representative': 49, 'size': 54}
id: 137000626
{'aut_label': '12B1', 'centralizer': '54.a1.b1', 'counter': 39, 'group_counter': 3557, 'group_order': 1944, 'label': '12B1', 'order': 12, 'powers': [26, 24], 'representative': 1494, 'size': 54}
id: 137000628
{'aut_label': '12B-1', 'centralizer': '54.a1.b1', 'counter': 40, 'group_counter': 3557, 'group_order': 1944, 'label': '12B-1', 'order': 12, 'powers': [27, 24], 'representative': 354, 'size': 54}
id: 137000629
{'aut_label': '12B-1', 'centralizer': '54.a1.a1', 'counter': 41, 'group_counter': 3557, 'group_order': 1944, 'label': '12C1', 'order': 12, 'powers': [26, 23], 'representative': 217, 'size': 54}
id: 137000630
{'aut_label': '12B1', 'centralizer': '54.a1.a1', 'counter': 42, 'group_counter': 3557, 'group_order': 1944, 'label': '12C-1', 'order': 12, 'powers': [27, 23], 'representative': 157, 'size': 54}
id: 137000631
{'aut_label': '12A1', 'centralizer': '54.a1.b1', 'counter': 43, 'group_counter': 3557, 'group_order': 1944, 'label': '12D1', 'order': 12, 'powers': [29, 24], 'representative': 478, 'size': 54}
id: 137000632
{'aut_label': '12A1', 'centralizer': '54.a1.b1', 'counter': 44, 'group_counter': 3557, 'group_order': 1944, 'label': '12D5', 'order': 12, 'powers': [29, 24], 'representative': 470, 'size': 54}
id: 137000633
{'aut_label': '12E1', 'centralizer': '54.a1.a1', 'counter': 45, 'group_counter': 3557, 'group_order': 1944, 'label': '12E1', 'order': 12, 'powers': [30, 23], 'representative': 1325, 'size': 54}
id: 137000634
{'aut_label': '12E-1', 'centralizer': '54.a1.a1', 'counter': 46, 'group_counter': 3557, 'group_order': 1944, 'label': '12E-1', 'order': 12, 'powers': [31, 23], 'representative': 713, 'size': 54}
id: 137000635
{'aut_label': '12E-1', 'centralizer': '54.a1.a1', 'counter': 47, 'group_counter': 3557, 'group_order': 1944, 'label': '12E5', 'order': 12, 'powers': [31, 23], 'representative': 701, 'size': 54}
id: 137000636
{'aut_label': '12E1', 'centralizer': '54.a1.a1', 'counter': 48, 'group_counter': 3557, 'group_order': 1944, 'label': '12E-5', 'order': 12, 'powers': [30, 23], 'representative': 1337, 'size': 54}
id: 137000637
{'aut_label': '12E1', 'centralizer': '54.a1.b1', 'counter': 49, 'group_counter': 3557, 'group_order': 1944, 'label': '12F1', 'order': 12, 'powers': [32, 24], 'representative': 1934, 'size': 54}
id: 137000639
{'aut_label': '12E-1', 'centralizer': '54.a1.b1', 'counter': 50, 'group_counter': 3557, 'group_order': 1944, 'label': '12F-1', 'order': 12, 'powers': [33, 24], 'representative': 1498, 'size': 54}
id: 137000640
{'aut_label': '12E-1', 'centralizer': '54.a1.b1', 'counter': 51, 'group_counter': 3557, 'group_order': 1944, 'label': '12F5', 'order': 12, 'powers': [33, 24], 'representative': 646, 'size': 54}
id: 137000641
{'aut_label': '12E1', 'centralizer': '54.a1.b1', 'counter': 52, 'group_counter': 3557, 'group_order': 1944, 'label': '12F-5', 'order': 12, 'powers': [32, 24], 'representative': 842, 'size': 54}
id: 137000642
{'aut_label': '12G1', 'centralizer': '162.b1.a1', 'counter': 53, 'group_counter': 3557, 'group_order': 1944, 'label': '12G1', 'order': 12, 'powers': [27, 25], 'representative': 203, 'size': 162}
id: 137000643
{'aut_label': '12G1', 'centralizer': '162.b1.a1', 'counter': 54, 'group_counter': 3557, 'group_order': 1944, 'label': '12G-1', 'order': 12, 'powers': [26, 25], 'representative': 1079, 'size': 162}

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: 12112218
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.1a', '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], 'schur_index': 1}
id: 12112229
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.1b', '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], 'schur_index': 1}
id: 12112240
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.1c', '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], 'schur_index': 1}
id: 12112243
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.1d', '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], 'schur_index': 1}
id: 12112244
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 2, 2, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112245
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 2, 0, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 2, 2, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
id: 12112246
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -2, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, 1, 1, 0, 0, -2, -2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112247
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, -2, 0, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, -2, -2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
id: 12112248
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.2e', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [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, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 12112219
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.2f', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, -4, 4, 4, -2, 4, -2, -2, 4, 4, -2, -2, -2, 4, -2, -2, 4, 4, -2, -2, -2, -2, 0, 0, 0, -4, -4, 2, -4, 2, 2, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 12112220
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.2g', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, -2, 4, 4, -2, -2, -2, -2, -2, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, -4, -4, -4, 2, -4, -4, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 12112225
{'cdim': 4, 'counter': 16, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 1, 1, 1, 4, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112226
{'cdim': 4, 'counter': 17, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.4b', 'multiplicity': 1, 'nt': [24, 62], 'qdim': 4, 'qvalues': [4, -4, 4, 4, -2, -2, -2, -2, -2, -2, 1, 1, 1, 4, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, -4, -4, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 12112221
{'cdim': 3, 'counter': 12, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.3a', 'multiplicity': 2, 'nt': [27, 83], 'qdim': 6, 'qvalues': [6, -2, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, -2, -2, 1, 1, 1, 1, -2, 1, 1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 12112222
{'cdim': 3, 'counter': 13, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.3b', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 6, 'qvalues': [6, -2, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 1, 1, -2, -2, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
id: 12112223
{'cdim': 3, 'counter': 14, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.3c', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 6, 'qvalues': [6, -2, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 1, 1, -2, -2, 1, 1, 1, 1, -2, 1, 1, -2, -2, -1, -1, 1, 1, 2, 2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
id: 12112224
{'cdim': 3, 'counter': 15, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.3d', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 6, 'qvalues': [6, -2, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, -2, 1, 1, 2, 2, 1, 1, -1, -1, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 12112235
{'cdim': 8, 'counter': 25, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.8a', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112227
{'cdim': 6, 'counter': 18, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.6a', 'multiplicity': 2, 'nt': [27, 83], 'qdim': 12, 'qvalues': [12, 4, -6, -6, 12, 12, -6, -6, -6, -6, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 4, -2, -2, -2, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112228
{'cdim': 6, 'counter': 19, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.6b', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 12, 'qvalues': [12, -4, -6, -6, -6, 12, 3, 3, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, -4, -1, -1, 2, 2, 2, -1, -1, -2, -2, 0, 0, -2, -2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112230
{'cdim': 6, 'counter': 20, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.6c', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 12, 'qvalues': [12, -4, -6, -6, 12, -6, -6, -6, 3, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 2, -4, 2, 2, 2, -1, -1, 2, -1, -1, 0, 0, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
id: 12112231
{'cdim': 6, 'counter': 21, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.6d', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -4, -6, -6, -6, 12, 3, 3, -6, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 2, 2, -4, -1, -1, 2, 2, 2, -1, -1, 2, 2, 0, 0, 2, 2, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112232
{'cdim': 6, 'counter': 22, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.6e', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -4, -6, -6, 12, -6, -6, -6, 3, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 2, -4, 2, 2, 2, -1, -1, 2, -1, -1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
id: 12112236
{'cdim': 8, 'counter': 26, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.8b', 'multiplicity': 2, 'nt': [24, 566], 'qdim': 16, 'qvalues': [16, 0, 16, 16, -8, 16, -8, -8, 16, 16, -8, -8, -8, -2, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112237
{'cdim': 8, 'counter': 27, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.8c', 'multiplicity': 2, 'nt': [24, 566], 'qdim': 16, 'qvalues': [16, 0, 16, 16, 16, -8, 16, 16, -8, -8, -8, -8, -8, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112238
{'cdim': 8, 'counter': 28, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.8d', 'multiplicity': 2, 'nt': [24, 1543], 'qdim': 16, 'qvalues': [16, 0, 16, 16, -8, -8, -8, -8, -8, -8, 4, 4, 4, -2, 1, 1, 1, 1, -5, -5, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112239
{'cdim': 8, 'counter': 29, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.8e', 'multiplicity': 2, 'nt': [24, 1543], 'qdim': 16, 'qvalues': [16, 0, 16, 16, -8, -8, -8, -8, -8, -8, 4, 4, 4, -2, 1, 1, 1, 1, 4, 4, -5, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112233
{'cdim': 6, 'counter': 23, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.6f', 'multiplicity': 4, 'nt': [36, 1223], 'qdim': 24, 'qvalues': [24, 8, -12, -12, -12, 24, 6, 6, -12, -12, -12, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 8, 2, 2, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112234
{'cdim': 6, 'counter': 24, 'faithful': False, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.6g', 'multiplicity': 4, 'nt': [36, 1223], 'qdim': 24, 'qvalues': [24, 8, -12, -12, 24, -12, -12, -12, 6, 6, -12, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 8, -4, -4, -4, 2, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112241
{'cdim': 12, 'counter': 30, 'faithful': True, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.12a', 'multiplicity': 2, 'nt': [36, 2997], 'qdim': 24, 'qvalues': [24, 8, -12, -12, -12, -12, 6, 6, 6, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 12112242
{'cdim': 12, 'counter': 31, 'faithful': True, 'group': '1944.3557', 'group_order': 1944, 'image': None, 'label': '1944.3557.12b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -12, -12, -12, -12, 6, 6, 6, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 27682044
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1944, 'label': '1944.3557.1a', '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]]]}
id: 27682055
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 972, 'label': '1944.3557.1b', '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]]]}
id: 27682066
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 972, 'label': '1944.3557.1c', '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]]]}
id: 27682077
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 972, 'label': '1944.3557.1d', '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]]]}
id: 27682088
{'center': '6.a1.b1', 'center_index': 6, 'center_order': 324, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.b1', 'kernel_order': 324, 'label': '1944.3557.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682094
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 324, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 324, 'label': '1944.3557.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
id: 27682095
{'center': '6.a1.b1', 'center_index': 6, 'center_order': 324, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 162, 'label': '1944.3557.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682096
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 324, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 162, 'label': '1944.3557.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
id: 27682097
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 486, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.a1.a1', 'kernel_order': 243, 'label': '1944.3557.2e', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27682045
{'center': '12.a1.b1', 'center_index': 12, 'center_order': 162, 'counter': 10, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.b1', 'kernel_order': 81, 'label': '1944.3557.2f1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682046
{'center': '12.a1.b1', 'center_index': 12, 'center_order': 162, 'counter': 11, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.b1', 'kernel_order': 81, 'label': '1944.3557.2f2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682047
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 162, 'counter': 12, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.a1', 'kernel_order': 81, 'label': '1944.3557.2g1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
id: 27682048
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 162, 'counter': 13, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.a1', 'kernel_order': 81, 'label': '1944.3557.2g2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
id: 27682049
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 14, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.3a1', 'nt': [27, 83], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-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]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
id: 27682050
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 15, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.3a2', 'nt': [27, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-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]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
id: 27682051
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 16, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.3b1', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-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]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]]]}
id: 27682052
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 17, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.3b2', 'nt': [54, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-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]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]]]}
id: 27682053
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 18, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.3c1', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-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]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]]]}
id: 27682054
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 19, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.3c2', 'nt': [54, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-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]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]]]}
id: 27682056
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 20, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.3d1', 'nt': [54, 0], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-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]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
id: 27682057
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 21, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.3d2', 'nt': [54, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-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]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
id: 27682058
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id: 27682059
{'center': '36.a1.a1', 'center_index': 36, 'center_order': 54, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '72.24', 'image_order': 72, 'indicator': -1, 'kernel': '72.b1.a1', 'kernel_order': 27, 'label': '1944.3557.4b', 'nt': [24, 62], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682060
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 24, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.6a1', 'nt': [27, 83], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 1]], [[6, -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]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682061
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 25, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.88', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 9, 'label': '1944.3557.6a2', 'nt': [27, 2], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, -1]], [[6, 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]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682062
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 26, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.b1', 'kernel_order': 3, 'label': '1944.3557.6b1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[6, 0]], [[-3, 1]], [[-3, -1]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682063
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 27, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.b1', 'kernel_order': 3, 'label': '1944.3557.6b2', 'nt': [54, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[6, 0]], [[-3, -1]], [[-3, 1]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682064
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 9, 'counter': 28, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.a1', 'kernel_order': 3, 'label': '1944.3557.6c1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[-3, 0]], [[6, 1]], [[6, -1]], [[-3, -1]], [[-3, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
id: 27682065
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 9, 'counter': 29, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.a1', 'kernel_order': 3, 'label': '1944.3557.6c2', 'nt': [54, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[-3, 0]], [[6, -1]], [[6, 1]], [[-3, 1]], [[-3, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
id: 27682067
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 30, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.b1', 'kernel_order': 3, 'label': '1944.3557.6d1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[6, 0]], [[-3, 1]], [[-3, -1]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682068
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 31, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.b1', 'kernel_order': 3, 'label': '1944.3557.6d2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[6, 0]], [[-3, -1]], [[-3, 1]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682069
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id: 27682070
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id: 27682071
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 34, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.b1', 'kernel_order': 3, 'label': '1944.3557.6f1', 'nt': [36, 1223], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[6, 0]], [[-3, 4]], [[3, 2]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[-3, 4]], [[3, 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]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[2, 0]], [[1, 2]], [[-1, 4]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682072
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 35, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.b1', 'kernel_order': 3, 'label': '1944.3557.6f2', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[6, 0]], [[3, 2]], [[-3, 4]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[2, 0]], [[-1, 4]], [[1, 2]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682073
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 36, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.b1', 'kernel_order': 3, 'label': '1944.3557.6f3', 'nt': [36, 1223], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[6, 0]], [[-3, 4]], [[3, 2]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[-3, 4]], [[3, 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]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[2, 0]], [[1, 2]], [[-1, 4]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682074
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 37, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.b1', 'kernel_order': 3, 'label': '1944.3557.6f4', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[6, 0]], [[3, 2]], [[-3, 4]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[2, 0]], [[-1, 4]], [[1, 2]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682075
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 9, 'counter': 38, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.a1', 'kernel_order': 3, 'label': '1944.3557.6g1', 'nt': [36, 1223], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-6, 2]], [[6, 4]], [[6, 0]], [[-3, 0]], [[6, 4]], [[-6, 2]], [[3, 2]], [[-3, 4]], [[-3, 0]], [[-3, 4]], [[3, 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]], [[2, 4]], [[-2, 2]], [[2, 0]], [[-1, 0]], [[-2, 2]], [[2, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]]]}
id: 27682076
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 9, 'counter': 39, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.a1', 'kernel_order': 3, 'label': '1944.3557.6g2', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[6, 4]], [[-6, 2]], [[6, 0]], [[-3, 0]], [[-6, 2]], [[6, 4]], [[-3, 4]], [[3, 2]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[2, 0]], [[-1, 0]], [[2, 4]], [[-2, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]]]}
id: 27682078
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 9, 'counter': 40, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.a1', 'kernel_order': 3, 'label': '1944.3557.6g3', 'nt': [36, 1223], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[-6, 2]], [[6, 4]], [[6, 0]], [[-3, 0]], [[6, 4]], [[-6, 2]], [[3, 2]], [[-3, 4]], [[-3, 0]], [[-3, 4]], [[3, 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]], [[2, 4]], [[-2, 2]], [[2, 0]], [[-1, 0]], [[-2, 2]], [[2, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]]]}
id: 27682079
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 9, 'counter': 41, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.553', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1.a1', 'kernel_order': 3, 'label': '1944.3557.6g4', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[2, 0]], [[6, 4]], [[-6, 2]], [[6, 0]], [[-3, 0]], [[-6, 2]], [[6, 4]], [[-3, 4]], [[3, 2]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[2, 0]], [[-1, 0]], [[2, 4]], [[-2, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]]]}
id: 27682080
{'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 42, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 27, 'label': '1944.3557.8a', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27682081
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 43, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.b1', 'kernel_order': 9, 'label': '1944.3557.8b1', 'nt': [24, 566], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682082
{'center': '216.a1.b1', 'center_index': 216, 'center_order': 9, 'counter': 44, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.b1', 'kernel_order': 9, 'label': '1944.3557.8b2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682083
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 9, 'counter': 45, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 9, 'label': '1944.3557.8c1', 'nt': [24, 566], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682084
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 9, 'counter': 46, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '216.161', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 9, 'label': '1944.3557.8c2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682085
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 47, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.729', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.3557.8d1', 'nt': [24, 1543], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682086
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 48, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.729', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.3557.8d2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682087
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 49, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.729', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.3557.8e1', 'nt': [24, 1543], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[-1, 0], [3, 1]], [[-4, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682089
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 50, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '648.729', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.3557.8e2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0]], [[2, 0]], [[-4, 0], [-3, 1]], [[-1, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682090
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 51, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.3557', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1.a1', 'kernel_order': 1, 'label': '1944.3557.12a1', 'nt': [36, 2997], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[12, -1]], [[12, 1]], [[-6, 0]], [[-6, 0]], [[-6, 1]], [[-6, -1]], [[-6, -1]], [[-6, 1]], [[3, 0]], [[3, 1]], [[3, -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]], [[4, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682091
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 52, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.3557', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1.a1', 'kernel_order': 1, 'label': '1944.3557.12a2', 'nt': [36, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[12, 1]], [[12, -1]], [[-6, 0]], [[-6, 0]], [[-6, -1]], [[-6, 1]], [[-6, 1]], [[-6, -1]], [[3, 0]], [[3, -1]], [[3, 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]], [[4, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682092
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 53, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.3557', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1.a1', 'kernel_order': 1, 'label': '1944.3557.12b1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, -1]], [[12, 1]], [[-6, 0]], [[-6, 0]], [[-6, 1]], [[-6, -1]], [[-6, -1]], [[-6, 1]], [[3, 0]], [[3, 1]], [[3, -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]], [[-4, 1]], [[-4, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 27682093
{'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 54, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.3557', 'group_counter': 3557, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.3557', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1.a1', 'kernel_order': 1, 'label': '1944.3557.12b2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, 1]], [[12, -1]], [[-6, 0]], [[-6, 0]], [[-6, -1]], [[-6, 1]], [[-6, 1]], [[-6, -1]], [[3, 0]], [[3, -1]], [[3, 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]], [[-4, -1]], [[-4, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema

id: 107649143
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1944, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1944.3557.1.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': '1944.3557', 'subgroup_hash': 3557, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 107649246
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 972, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.768', 'subgroup_hash': 768, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3):C_{12}', 'supersolvable': False, 'sylow': 0}
id: 107649257
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 972, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.768', 'subgroup_hash': 768, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3):C_{12}', 'supersolvable': False, 'sylow': 0}
id: 107649268
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 972, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.773', 'subgroup_hash': 773, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
id: 107649279
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.553', 'subgroup_hash': 553, 'subgroup_order': 648, 'subgroup_tex': 'C_3:\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 107649290
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.3.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.553', 'subgroup_hash': 553, 'subgroup_order': 648, 'subgroup_tex': 'C_3:\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 107649301
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 486, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': ['D', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
id: 107649312
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
id: 107649323
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
id: 107649144
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 162, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '324.110', 'subgroup_hash': 110, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 107649155
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 162, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.110', 'subgroup_hash': 110, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 107649166
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
id: 107649177
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
id: 107649188
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
id: 107649199
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 243, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1944.3557.8.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': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': ['F', 'L2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 3}
id: 107649210
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.123', 'subgroup_hash': 123, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 107649221
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.88', 'subgroup_hash': 88, 'subgroup_order': 216, 'subgroup_tex': '\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 107649232
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 162, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
id: 107649243
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 162, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
id: 107649247
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649248
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 54, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
id: 107649249
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649250
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649251
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.18.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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649252
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
id: 107649253
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
id: 107649254
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
id: 107649255
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649256
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649258
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649259
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649260
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
id: 107649261
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.24.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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649262
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649263
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.24.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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649264
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
id: 107649265
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.27.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
id: 107649266
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
id: 107649267
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 54, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
id: 107649269
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 107649270
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649271
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649272
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649273
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649274
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649275
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649276
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649277
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.e1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.b2', '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649278
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649280
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649281
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.g1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649282
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.g1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a3', '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649283
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.36.g1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a4', '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649284
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649285
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649286
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649287
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649288
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649289
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649291
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649292
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649293
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649294
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649295
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649296
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 107649297
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 27, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649298
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 27, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.24', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649299
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649300
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649302
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649303
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649304
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649305
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649306
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649307
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649308
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649309
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649310
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649311
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649313
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649314
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649315
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649316
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.i1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649317
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.i2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649318
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.i2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
id: 107649319
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649320
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649321
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649322
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.j1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649324
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649325
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649326
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649327
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.l1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1.a3', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649328
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.72.l1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1.a4', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 107649329
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 107649330
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.81.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 107649331
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.81.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 107649332
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 107649333
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 107649145
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 107649146
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 107649147
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 107649148
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 107649149
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 107649150
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649151
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649152
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649153
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649154
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649156
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649157
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.h1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649158
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649159
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649160
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649161
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649162
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649163
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.108.j1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 107649164
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 118, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649165
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.162.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649167
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649168
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649169
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.162.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649170
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.162.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 107649171
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.162.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 107649172
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.162.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 107649173
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.162.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 107649174
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.162.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649175
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.162.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 107649176
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.162.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 107649178
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 9, 'counter': 130, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.161', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649179
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 9, 'counter': 131, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.216.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.161', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649180
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 9, 'counter': 132, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3557.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.88', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 88, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SU(3,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649181
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649182
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649183
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649184
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649185
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649186
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649187
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649189
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649190
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649191
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649192
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649193
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649194
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649195
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649196
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649197
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.j1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649198
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649200
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.k1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649201
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649202
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.k1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649203
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649204
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649205
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649206
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649207
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649208
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649209
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649211
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649212
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.o1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649213
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649214
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649215
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649216
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.216.p1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 107649217
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1944.3557.243.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 2}
id: 107649218
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 167, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 107649219
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 107649220
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.324.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 107649222
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 107649223
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.324.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 107649224
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.324.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 107649225
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.324.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 107649226
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3557.324.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 107649227
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.486.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 107649228
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.486.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 107649229
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.486.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 107649230
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 3, 'counter': 178, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3557.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.729', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 729, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:Q_8', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', 'D3', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649231
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 3, 'counter': 179, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3557.648.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.553', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 553, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:\\SU(3,2)', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649233
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 3, 'counter': 180, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3557.648.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.553', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 553, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:\\SU(3,2)', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649234
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649235
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649236
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649237
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649238
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649239
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649240
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.g1.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649241
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649242
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.648.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 107649244
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3557.972.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 107649245
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3557', 'ambient_counter': 3557, 'ambient_order': 1944, 'ambient_tex': 'C_3^2:\\SU(3,2)', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 1, 'counter': 191, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1944.3557.1944.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1944.3557', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3557, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:\\SU(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D4', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

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

gps_subgroup_data • Show schema

id: 107649143
{'ambient': '1944.3557', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1.a1', 'complements': ['1944.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '3.a1.a1', '3.a1.b1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7710, 5098, 8022, 5000, 6590, 4753, 2741, 5000], 'generators': [1, 24, 72, 6, 8, 648, 1512, 12], 'label': '1944.3557.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '648.729'}
id: 107649144
{'ambient': '1944.3557', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.187', 'aut_weyl_index': 36, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.c1.a1', '54.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7806, -1, 8163, -1, 5412, -1, 2477, -1], 'generators': [1, 648, 1512, 24, 12, 1800], 'label': '1944.3557.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649145
{'ambient': '1944.3557', 'aut_centralizer_order': 72, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.d1.a1', '36.d1.b1', '54.d1.a1'], 'contains': ['216.c1.a1', '324.a1.a1', '324.d1.a1', '324.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5236, -1, 5839, -1, 5806, -1, 4916, -1], 'generators': [12, 32, 648], 'label': '1944.3557.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649146
{'ambient': '1944.3557', 'aut_centralizer_order': 72, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.e1.a1', '36.e1.a2', '54.e1.a1'], 'contains': ['216.g1.a1', '324.b1.a1', '324.c1.b1', '324.e1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7459, -1, 7317, -1, 6218, -1, 3299, -1], 'generators': [12, 656, 24], 'label': '1944.3557.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '108.c1.a1', 'projective_image': '1944.3557', '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': '2.1'}
id: 107649147
{'ambient': '1944.3557', 'aut_centralizer_order': 72, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.e1.b1', '36.e1.b2', '54.e1.b1'], 'contains': ['216.g1.b1', '324.b1.b1', '324.c1.a1', '324.e1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7459, -1, 8428, -1, 6218, -1, 3502, -1], 'generators': [12, 8, 672], 'label': '1944.3557.108.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '108.c1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649148
{'ambient': '1944.3557', 'aut_centralizer_order': 72, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 648, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.f1.a1', '54.f1.a1', '54.f1.b1', '54.g1.a1'], 'contains': ['216.b1.a1', '324.b1.a1', '324.b1.b1', '324.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8567, -1, 8668, -1, 7042, -1, 2690, -1], 'generators': [12, 8, 24], 'label': '1944.3557.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.d1.a1', 'projective_image': '1944.3557', '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': '4.2'}
id: 107649149
{'ambient': '1944.3557', 'aut_centralizer_order': 72, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.g1.a1', '36.g1.a2', '36.g1.a3', '36.g1.a4'], 'contains': ['216.l1.a1', '324.c1.a1', '324.c1.b1', '324.d1.a1', '324.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6844, -1, 8174, -1, 5394, -1, 4713, -1], 'generators': [12, 656, 672], 'label': '1944.3557.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '108.e1.a1', 'projective_image': '1944.3557', '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': '1.1'}
id: 107649150
{'ambient': '1944.3557', 'aut_centralizer_order': 36, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.c1.a1', '36.c1.b1', '36.d1.a1', '36.d1.b1'], 'contains': ['216.d1.a1', '324.a1.a1', '324.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4083, -1, 4454, -1, 3347, -1, 6529, -1], 'generators': [12, 648, 720], 'label': '1944.3557.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.f1.a1', 'projective_image': '648.729', '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': '6.1'}
id: 107649151
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.e1.a1', '36.e1.a2', '36.f1.a1'], 'contains': ['216.h1.a1', '324.b1.a1', '324.f1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5742, -1, 6957, -1, 4983, -1, 3906, -1], 'generators': [12, 24, 720], 'label': '1944.3557.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.g1.a1', 'projective_image': '1944.3557', '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: 107649152
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '36.e1.b1', '36.e1.b2', '36.f1.a1'], 'contains': ['216.h1.b1', '324.b1.b1', '324.f1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5742, -1, 7451, -1, 4983, -1, 3705, -1], 'generators': [12, 8, 720], 'label': '1944.3557.108.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.g1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649153
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.e1.b1', '36.g1.a1', '36.g1.a2'], 'contains': ['216.j1.a1', '324.c1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4911, -1, 7196, -1, 4574, -1, 4510, -1], 'generators': [12, 1320, 720], 'label': '1944.3557.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.h1.a1', 'projective_image': '1944.3557', '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: 107649154
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.e1.b2', '36.g1.a3', '36.g1.a4'], 'contains': ['216.j1.a2', '324.c1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4911, -1, 7078, -1, 4574, -1, 5320, -1], 'generators': [12, 672, 720], 'label': '1944.3557.108.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.h1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649155
{'ambient': '1944.3557', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.187', 'aut_weyl_index': 36, 'centralizer': '216.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.b1'], 'contains': ['12.a1.b1', '18.c1.b1', '54.a1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7806, -1, 7490, -1, 5412, -1, 2993, -1], 'generators': [6, 648, 1512, 8, 12, 288], 'label': '1944.3557.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.b1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649156
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '36.e1.a1', '36.g1.a1', '36.g1.a3'], 'contains': ['216.j1.b1', '324.c1.b1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4911, -1, 6467, -1, 4574, -1, 4309, -1], 'generators': [12, 656, 720], 'label': '1944.3557.108.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.h1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649157
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '36.e1.a2', '36.g1.a2', '36.g1.a4'], 'contains': ['216.j1.b2', '324.c1.b1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4911, -1, 6713, -1, 4574, -1, 4108, -1], 'generators': [12, 1304, 720], 'label': '1944.3557.108.h1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.h1.b2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649158
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.f1.a1', '36.g1.a2', '36.g1.a3'], 'contains': ['216.m1.a1', '324.d1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6064, -1, 6837, -1, 4165, -1, 6126, -1], 'generators': [12, 32, 864], 'label': '1944.3557.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.i1.a1', 'projective_image': '1944.3557', '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': '6.1'}
id: 107649159
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.b1', '36.f1.a1', '36.g1.a1', '36.g1.a4'], 'contains': ['216.m1.b1', '324.d1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6064, -1, 6594, -1, 4165, -1, 6327, -1], 'generators': [12, 32, 720], 'label': '1944.3557.108.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.i1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649160
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.e1.a1', '36.e1.b1', '36.g1.a4'], 'contains': ['216.o1.a1', '324.e1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4405, -1, 5959, -1, 3756, -1, 5723, -1], 'generators': [12, 1328, 864], 'label': '1944.3557.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.j1.a1', 'projective_image': '1944.3557', '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': '6.1'}
id: 107649161
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.e1.a2', '36.e1.b2', '36.g1.a1'], 'contains': ['216.o1.a2', '324.e1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4405, -1, 5599, -1, 3756, -1, 5119, -1], 'generators': [12, 680, 864], 'label': '1944.3557.108.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.j1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649162
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.b1', '36.e1.a1', '36.e1.b2', '36.g1.a2'], 'contains': ['216.o1.b1', '324.e1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4405, -1, 6247, -1, 3756, -1, 5522, -1], 'generators': [12, 680, 720], 'label': '1944.3557.108.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.j1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649163
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.b1', '36.e1.a2', '36.e1.b1', '36.g1.a3'], 'contains': ['216.o1.b2', '324.e1.a1', '324.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4405, -1, 5719, -1, 3756, -1, 5925, -1], 'generators': [12, 1328, 720], 'label': '1944.3557.108.j1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.j1.b2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649164
{'ambient': '1944.3557', 'aut_centralizer_order': 48, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '54.a1.a1', '54.b1.b1', '81.a1.a1'], 'contains': ['324.a1.a1', '486.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8025, -1, 7897, -1, 7926, -1, 1364, -1], 'generators': [1, 648, 12], 'label': '1944.3557.162.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649165
{'ambient': '1944.3557', 'aut_centralizer_order': 48, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '54.a1.b1', '54.b1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '486.a1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8025, -1, 7541, -1, 7926, -1, 1849, -1], 'generators': [6, 648, 12], 'label': '1944.3557.162.a1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.b1', 'old_label': '162.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649166
{'ambient': '1944.3557', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.742', 'aut_weyl_index': 12, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.d1.a1', '54.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6616, -1, 7689, -1, 6921, -1, 4121, -1], 'generators': [3, 648, 1512, 12, 24, 720], 'label': '1944.3557.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
id: 107649167
{'ambient': '1944.3557', 'aut_centralizer_order': 16, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '162.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '54.c1.a1', '54.c1.b1', '54.d1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '486.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [7090, -1, 7618, -1, 8192, -1, 2386, -1], 'generators': [3, 648, 12], 'label': '1944.3557.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649168
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.f1.a1', '81.b1.a1'], 'contains': ['324.b1.a1', '486.a1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9706, -1, 9462, -1, 8737, -1, 1126, -1], 'generators': [1, 24, 12], 'label': '1944.3557.162.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.c1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649169
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.b1', '54.f1.b1', '81.b1.b1'], 'contains': ['324.b1.b1', '486.a1.b1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [9706, -1, 9136, -1, 8737, -1, 1580, -1], 'generators': [6, 8, 12], 'label': '1944.3557.162.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.b1', 'old_label': '162.c1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649170
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '54.e1.a1', '54.f1.b1', '81.b1.a1'], 'contains': ['324.b1.a1', '486.a1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9453, -1, 8907, -1, 8465, -1, 1715, -1], 'generators': [6, 12, 24], 'label': '1944.3557.162.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '162.d1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649171
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.b1', '54.e1.b1', '54.f1.a1', '81.b1.b1'], 'contains': ['324.b1.b1', '486.a1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9453, -1, 9769, -1, 8465, -1, 706, -1], 'generators': [1, 12, 8], 'label': '1944.3557.162.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '162.d1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649172
{'ambient': '1944.3557', 'aut_centralizer_order': 8, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.g1.a1', '81.b1.a1'], 'contains': ['324.b1.a1', '486.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9143, -1, 9215, -1, 9010, -1, 2252, -1], 'generators': [3, 12, 24], 'label': '1944.3557.162.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.e1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649173
{'ambient': '1944.3557', 'aut_centralizer_order': 8, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.b1', '54.g1.a1', '81.b1.b1'], 'contains': ['324.b1.b1', '486.b1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [9143, -1, 9296, -1, 9010, -1, 2115, -1], 'generators': [3, 12, 8], 'label': '1944.3557.162.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.b1', 'old_label': '162.e1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649174
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.e1.b1'], 'contains': ['324.c1.a1', '486.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8727, -1, 9004, -1, 7381, -1, 994, -1], 'generators': [1, 672, 12], 'label': '1944.3557.162.f1.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': '162.f1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649175
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.b1', '54.e1.a1'], 'contains': ['324.c1.b1', '486.a1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8727, -1, 8666, -1, 7381, -1, 1980, -1], 'generators': [6, 656, 12], 'label': '1944.3557.162.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.b1', 'old_label': '162.f1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649176
{'ambient': '1944.3557', 'aut_centralizer_order': 8, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '54.g1.a1'], 'contains': ['324.d1.a1', '486.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8513, -1, 8745, -1, 7653, -1, 2520, -1], 'generators': [3, 12, 32], 'label': '1944.3557.162.g1.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': '162.g1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649177
{'ambient': '1944.3557', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.742', 'aut_weyl_index': 12, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.b1'], 'contains': ['12.a1.b1', '18.d1.a1', '54.c1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6616, -1, 7896, -1, 6921, -1, 3772, -1], 'generators': [3, 648, 1512, 12, 8, 720], 'label': '1944.3557.6.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.c1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
id: 107649178
{'ambient': '1944.3557', 'aut_centralizer_order': 1296, 'aut_label': '216.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.c1.a1', '72.d1.a1', '108.a1.a1'], 'contains': ['648.a1.a1', '648.b1.a1', '648.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5888, 3743, 6783, 4041, 3596, 4478, 6080, 4275], 'generators': [24, 648], 'label': '1944.3557.216.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['24.a1.a1', '72.a1.a1'], 'normal_contains': ['648.a1.a1', '648.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '648.729', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.37', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649179
{'ambient': '1944.3557', 'aut_centralizer_order': 1296, 'aut_label': '216.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.c1.b1', '72.d1.b1', '108.a1.b1'], 'contains': ['648.a1.a1', '648.b1.b1', '648.c1.b1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5888, 3743, 5537, 5000, 3596, 4478, 5468, 3316], 'generators': [8, 648], 'label': '1944.3557.216.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '216.a1.b1', 'normal_contained_in': ['24.a1.b1', '72.a1.a1'], 'normal_contains': ['648.a1.a1', '648.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.b1', 'projective_image': '648.729', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.37', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649180
{'ambient': '1944.3557', 'aut_centralizer_order': 648, 'aut_label': '216.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 648, 'centralizer': '4.a1.a1', 'complements': ['9.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.k1.a1', '108.d1.a1'], 'contains': ['648.b1.a1', '648.b1.b1', '648.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6447, 2132, 7264, 5960, 4341, 2976, 5346, 2357], 'generators': [8, 24], 'label': '1944.3557.216.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['72.a1.a1'], 'normal_contains': ['648.b1.a1', '648.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '1944.3557', 'quotient_action_image': '4.2', 'quotient_action_kernel': '54.8', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 107649181
{'ambient': '1944.3557', 'aut_centralizer_order': 648, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.e1.a1', '72.e1.b1', '72.f1.a1', '72.f1.b1', '108.b1.a1'], 'contains': ['648.a1.a1', '648.d1.a1', '648.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3981, -1, 3184, -1, 3099, -1, 8404, -1], 'generators': [32, 648], 'label': '1944.3557.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '216.c1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649182
{'ambient': '1944.3557', 'aut_centralizer_order': 108, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.c1.a1', '72.c1.b1', '72.e1.a1', '72.e1.b1', '72.g1.a1', '72.g1.b1', '72.h1.a1', '72.h1.b1', '108.f1.a1'], 'contains': ['648.a1.a1', '648.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1562, -1, 1446, -1, 1113, -1, 9138, -1], 'generators': [72, 648], 'label': '1944.3557.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '216.d1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649183
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.d1.b1', '72.f1.a1', '72.f1.b1', '72.g1.a1', '72.i1.a1', '72.i1.a2', '72.i1.b1', '72.i1.b2', '72.i2.a1', '72.i2.a2'], 'contains': ['648.a1.a1', '648.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [795, -1, 791, -1, 865, -1, 9627, -1], 'generators': [96, 648], 'label': '1944.3557.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '216.e1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 107649184
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '72.d1.a1', '72.f1.a1', '72.f1.b1', '72.g1.b1', '72.i1.a1', '72.i1.a2', '72.i1.b1', '72.i1.b2', '72.i2.a1', '72.i2.a2'], 'contains': ['648.a1.a1', '648.g1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [795, -1, 389, -1, 865, -1, 9505, -1], 'generators': [80, 648], 'label': '1944.3557.216.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '216.e1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 107649185
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.d1.b1', '72.e1.a1', '72.f1.a1', '72.h1.a1', '72.h1.b1', '72.i1.a1', '72.i1.a2', '72.i2.a1', '72.i2.a2'], 'contains': ['648.a1.a1', '648.h1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [516, -1, 171, -1, 616, -1, 9382, -1], 'generators': [1544, 648], 'label': '1944.3557.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '216.f1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 107649186
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.d1.b1', '72.e1.b1', '72.f1.b1', '72.h1.a1', '72.h1.b1', '72.i1.b1', '72.i1.b2', '72.i2.a1', '72.i2.a2'], 'contains': ['648.a1.a1', '648.h1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [516, -1, 1060, -1, 616, -1, 9260, -1], 'generators': [104, 648], 'label': '1944.3557.216.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '216.f1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 107649187
{'ambient': '1944.3557', 'aut_centralizer_order': 648, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.j1.a1', '72.j1.a2', '108.c1.a1'], 'contains': ['648.b1.a1', '648.c1.b1', '648.e1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6643, -1, 4924, -1, 4092, -1, 5590, -1], 'generators': [656, 24], 'label': '1944.3557.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '216.g1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649188
{'ambient': '1944.3557', 'aut_centralizer_order': 1, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 6, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.c1.a1', '18.d1.a1', '54.d1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6058, -1, 7050, -1, 6097, -1, 5068, -1], 'generators': [3, 648, 1512, 12, 32, 720], 'label': '1944.3557.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '6.d1.a1', 'projective_image': '648.729', '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': '108.37'}
id: 107649189
{'ambient': '1944.3557', 'aut_centralizer_order': 648, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.j1.b1', '72.j1.b2', '108.c1.b1'], 'contains': ['648.b1.b1', '648.c1.a1', '648.e1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6643, -1, 6856, -1, 4092, -1, 5713, -1], 'generators': [8, 672], 'label': '1944.3557.216.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.g1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649190
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.j1.a1', '72.j1.a2', '72.k1.a1', '108.g1.a1'], 'contains': ['648.b1.a1', '648.f1.a1', '648.g1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3520, -1, 4242, -1, 3347, -1, 5957, -1], 'generators': [24, 72], 'label': '1944.3557.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.h1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649191
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '72.j1.b1', '72.j1.b2', '72.k1.a1', '108.g1.b1'], 'contains': ['648.b1.b1', '648.f1.a1', '648.g1.b1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3520, -1, 5338, -1, 3347, -1, 5835, -1], 'generators': [8, 72], 'label': '1944.3557.216.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.h1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649192
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.j1.a1', '72.j1.a2', '72.k1.a1'], 'contains': ['648.b1.a1', '648.g1.b1', '648.h1.a1', '648.h1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2151, -1, 1902, -1, 2106, -1, 7670, -1], 'generators': [80, 24], 'label': '1944.3557.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.i1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649193
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.b1', '72.j1.b1', '72.j1.b2', '72.k1.a1'], 'contains': ['648.b1.b1', '648.g1.a1', '648.h1.a1', '648.h1.b1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2151, -1, 3551, -1, 2106, -1, 8159, -1], 'generators': [8, 96], 'label': '1944.3557.216.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.i1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649194
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.j1.b1', '72.l1.a1', '72.l1.a2', '108.h1.a1'], 'contains': ['648.c1.a1', '648.f1.a1', '648.g1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2976, -1, 4852, -1, 2851, -1, 6447, -1], 'generators': [1320, 72], 'label': '1944.3557.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.j1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649195
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.j1.b2', '72.l1.a3', '72.l1.a4', '108.h1.a2'], 'contains': ['648.c1.a1', '648.f1.a1', '648.g1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2976, -1, 4700, -1, 2851, -1, 6814, -1], 'generators': [672, 72], 'label': '1944.3557.216.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.j1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649196
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '72.j1.a1', '72.l1.a1', '72.l1.a3', '108.h1.b1'], 'contains': ['648.c1.b1', '648.f1.a1', '648.g1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2976, -1, 4315, -1, 2851, -1, 6324, -1], 'generators': [656, 72], 'label': '1944.3557.216.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.j1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649197
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '72.j1.a2', '72.l1.a2', '72.l1.a4', '108.h1.b2'], 'contains': ['648.c1.b1', '648.f1.a1', '648.g1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2976, -1, 4482, -1, 2851, -1, 6202, -1], 'generators': [1304, 72], 'label': '1944.3557.216.j1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.j1.b2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649198
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.j1.b1', '72.l1.a1', '72.l1.a2'], 'contains': ['648.c1.a1', '648.g1.b1', '648.h1.a1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1918, -1, 2790, -1, 1609, -1, 8281, -1], 'generators': [80, 1320], 'label': '1944.3557.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.k1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649199
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '8.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '576.8300', 'aut_weyl_index': 9, 'centralizer': '72.a1.a1', 'complements': ['243.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['24.a1.a1', '24.a1.b1', '24.b1.a1', '24.b1.b1', '24.c1.a1', '24.d1.a1', '24.d1.b1', '24.e1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1697, 2721, 1543, 5000, 1727, 3288, 8477, 2661], 'generators': [8, 24, 72, 1512], 'label': '1944.3557.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['24.a1.a1', '24.a1.b1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '648.729', 'quotient_action_image': '8.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649200
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.j1.b2', '72.l1.a3', '72.l1.a4'], 'contains': ['648.c1.a1', '648.g1.b1', '648.h1.a1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1918, -1, 2234, -1, 1609, -1, 8893, -1], 'generators': [80, 672], 'label': '1944.3557.216.k1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.k1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649201
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.b1', '72.j1.a1', '72.l1.a1', '72.l1.a3'], 'contains': ['648.c1.b1', '648.g1.a1', '648.h1.a1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1918, -1, 2486, -1, 1609, -1, 9016, -1], 'generators': [656, 96], 'label': '1944.3557.216.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.k1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649202
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.b1', '72.j1.a2', '72.l1.a2', '72.l1.a4'], 'contains': ['648.c1.b1', '648.g1.a1', '648.h1.a1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1918, -1, 3112, -1, 1609, -1, 8771, -1], 'generators': [1304, 96], 'label': '1944.3557.216.k1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.k1.b2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649203
{'ambient': '1944.3557', 'aut_centralizer_order': 648, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.l1.a1', '72.l1.a2', '72.l1.a3', '72.l1.a4', '108.e1.a1'], 'contains': ['648.c1.a1', '648.c1.b1', '648.d1.a1', '648.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4525, -1, 5073, -1, 3844, -1, 6569, -1], 'generators': [656, 672], 'label': '1944.3557.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '216.l1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649204
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.k1.a1', '72.l1.a2', '72.l1.a3', '108.i1.a1'], 'contains': ['648.d1.a1', '648.f1.a1', '648.h1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3784, -1, 4568, -1, 2603, -1, 7303, -1], 'generators': [32, 1512], 'label': '1944.3557.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.m1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649205
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '72.k1.a1', '72.l1.a1', '72.l1.a4', '108.i1.b1'], 'contains': ['648.d1.a1', '648.f1.a1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3784, -1, 4387, -1, 2603, -1, 7425, -1], 'generators': [32, 72], 'label': '1944.3557.216.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.m1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649206
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.k1.a1', '72.l1.a1', '72.l1.a4'], 'contains': ['648.d1.a1', '648.g1.a1', '648.g1.b1', '648.h1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2779, -1, 2066, -1, 1858, -1, 8649, -1], 'generators': [152, 96], 'label': '1944.3557.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.n1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649207
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.b1', '72.k1.a1', '72.l1.a2', '72.l1.a3'], 'contains': ['648.d1.a1', '648.g1.a1', '648.g1.b1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2779, -1, 3459, -1, 1858, -1, 8526, -1], 'generators': [80, 96], 'label': '1944.3557.216.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.n1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649208
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.j1.a1', '72.j1.b1', '72.l1.a4', '108.j1.a1'], 'contains': ['648.e1.a1', '648.f1.a1', '648.h1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3323, -1, 3844, -1, 2354, -1, 7058, -1], 'generators': [1328, 1512], 'label': '1944.3557.216.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.o1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649209
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.j1.a2', '72.j1.b2', '72.l1.a1', '108.j1.a2'], 'contains': ['648.e1.a1', '648.f1.a1', '648.h1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3323, -1, 3282, -1, 2354, -1, 6691, -1], 'generators': [680, 1512], 'label': '1944.3557.216.o1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.o1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649210
{'ambient': '1944.3557', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.889', 'aut_weyl_index': 18, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['18.a1.a1', '18.a1.b1', '18.b1.a1', '27.a1.a1', '27.a1.b1', '27.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8966, -1, 8802, -1, 7947, -1, 1712, -1], 'generators': [1, 24, 8, 6, 648, 12], 'label': '1944.3557.9.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 107649211
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '72.j1.a1', '72.j1.b2', '72.l1.a2', '108.j1.b1'], 'contains': ['648.e1.a1', '648.f1.a1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3323, -1, 4080, -1, 2354, -1, 6936, -1], 'generators': [680, 72], 'label': '1944.3557.216.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.o1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649212
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '72.j1.a2', '72.j1.b1', '72.l1.a3', '108.j1.b2'], 'contains': ['648.e1.a1', '648.f1.a1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3323, -1, 3643, -1, 2354, -1, 7181, -1], 'generators': [1328, 72], 'label': '1944.3557.216.o1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.o1.b2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649213
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.j1.a1', '72.j1.b2', '72.l1.a2'], 'contains': ['648.e1.a1', '648.g1.a1', '648.g1.b1', '648.h1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2385, -1, 2382, -1, 1361, -1, 7792, -1], 'generators': [800, 96], 'label': '1944.3557.216.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.p1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649214
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.j1.a2', '72.j1.b1', '72.l1.a3'], 'contains': ['648.e1.a1', '648.g1.a1', '648.g1.b1', '648.h1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2385, -1, 1984, -1, 1361, -1, 8037, -1], 'generators': [1448, 96], 'label': '1944.3557.216.p1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.p1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649215
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.b1', '72.j1.a1', '72.j1.b1', '72.l1.a4'], 'contains': ['648.e1.a1', '648.g1.a1', '648.g1.b1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2385, -1, 3039, -1, 1361, -1, 7915, -1], 'generators': [728, 96], 'label': '1944.3557.216.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.p1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649216
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.b1', '72.j1.a2', '72.j1.b2', '72.l1.a1'], 'contains': ['648.e1.a1', '648.g1.a1', '648.g1.b1', '648.h1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2385, -1, 2653, -1, 1361, -1, 7548, -1], 'generators': [1376, 96], 'label': '1944.3557.216.p1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.p1.b2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649217
{'ambient': '1944.3557', 'aut_centralizer_order': 8, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 648, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1.a1', '81.b1.a1', '81.b1.b1'], 'contains': ['486.a1.a1', '486.a1.b1', '486.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9009, -1, 9110, -1, 9397, -1, 1245, -1], 'generators': [1, 6], 'label': '1944.3557.243.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': '243.a1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 107649218
{'ambient': '1944.3557', 'aut_centralizer_order': 288, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.a1.b1', '108.b1.a1', '108.f1.a1', '162.a1.a1', '162.a1.b1', '162.b1.a1'], 'contains': ['648.a1.a1', '972.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5335, -1, 6026, -1, 6036, -1, 3156, -1], 'generators': [12, 648], 'label': '1944.3557.324.a1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649219
{'ambient': '1944.3557', 'aut_centralizer_order': 144, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.c1.a1', '108.d1.a1', '108.g1.a1', '162.c1.a1', '162.d1.a1', '162.e1.a1'], 'contains': ['648.b1.a1', '972.a1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7966, -1, 8217, -1, 6630, -1, 3048, -1], 'generators': [12, 24], 'label': '1944.3557.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649220
{'ambient': '1944.3557', 'aut_centralizer_order': 144, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.b1', '108.c1.b1', '108.d1.a1', '108.g1.b1', '162.c1.b1', '162.d1.b1', '162.e1.b1'], 'contains': ['648.b1.b1', '972.a1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7966, -1, 8384, -1, 6630, -1, 2893, -1], 'generators': [12, 8], 'label': '1944.3557.324.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.b1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649221
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.a1.b1'], 'contains': ['18.c1.a1', '18.c1.b1', '18.d1.a1', '81.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7483, -1, 8031, -1, 7526, -1, 2763, -1], 'generators': [1, 648, 1512, 6, 12, 72], 'label': '1944.3557.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649222
{'ambient': '1944.3557', 'aut_centralizer_order': 144, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.c1.b1', '108.e1.a1', '108.h1.a1', '108.h1.a2', '162.f1.a1'], 'contains': ['648.c1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7240, -1, 7590, -1, 5600, -1, 4184, -1], 'generators': [12, 672], 'label': '1944.3557.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '324.c1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649223
{'ambient': '1944.3557', 'aut_centralizer_order': 144, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '18.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.b1', '108.c1.a1', '108.e1.a1', '108.h1.b1', '108.h1.b2', '162.f1.b1'], 'contains': ['648.c1.b1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7240, -1, 7026, -1, 5600, -1, 3751, -1], 'generators': [12, 656], 'label': '1944.3557.324.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '324.c1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649224
{'ambient': '1944.3557', 'aut_centralizer_order': 144, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.d1.a1', '108.e1.a1', '108.i1.a1', '108.i1.b1', '162.g1.a1'], 'contains': ['648.d1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7034, -1, 7121, -1, 5818, -1, 4815, -1], 'generators': [12, 32], 'label': '1944.3557.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '324.d1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649225
{'ambient': '1944.3557', 'aut_centralizer_order': 72, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.c1.a1', '108.c1.b1', '108.e1.a1', '108.j1.a1', '108.j1.a2', '108.j1.b1', '108.j1.b2'], 'contains': ['648.e1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5781, -1, 5808, -1, 5382, -1, 5021, -1], 'generators': [12, 680], 'label': '1944.3557.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '324.e1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649226
{'ambient': '1944.3557', 'aut_centralizer_order': 72, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '108.g1.a1', '108.g1.b1', '108.h1.a1', '108.h1.a2', '108.h1.b1', '108.h1.b2', '108.i1.a1', '108.i1.b1', '108.j1.a1', '108.j1.a2', '108.j1.b1', '108.j1.b2'], 'contains': ['648.f1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4649, -1, 6295, -1, 4574, -1, 5231, -1], 'generators': [12, 720], 'label': '1944.3557.324.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '324.f1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649227
{'ambient': '1944.3557', 'aut_centralizer_order': 48, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1.a1', '162.c1.a1', '162.d1.b1', '162.f1.a1', '243.a1.a1'], 'contains': ['972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8935, -1, 9152, -1, 7950, -1, 1185, -1], 'generators': [1], 'label': '1944.3557.486.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '486.a1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649228
{'ambient': '1944.3557', 'aut_centralizer_order': 48, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1.b1', '162.c1.b1', '162.d1.a1', '162.f1.b1', '243.a1.a1'], 'contains': ['972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8935, -1, 8867, -1, 7950, -1, 1782, -1], 'generators': [6], 'label': '1944.3557.486.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.b1', 'old_label': '486.a1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649229
{'ambient': '1944.3557', 'aut_centralizer_order': 32, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '162.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.b1.a1', '162.e1.a1', '162.e1.b1', '162.g1.a1', '243.a1.a1'], 'contains': ['972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8515, -1, 8983, -1, 8192, -1, 2319, -1], 'generators': [3], 'label': '1944.3557.486.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '486.b1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649230
{'ambient': '1944.3557', 'aut_centralizer_order': 2592, 'aut_label': '648.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.a1.b1', '216.c1.a1', '216.d1.a1', '216.e1.a1', '216.e1.b1', '216.f1.a1', '216.f1.b1', '324.a1.a1'], 'contains': ['1944.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2430, 4333, 1765, 4041, 2648, 5027, 8771, 4275], 'generators': [648], 'label': '1944.3557.648.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['72.b1.a1', '216.a1.a1', '216.a1.b1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '648.729', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.729', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649231
{'ambient': '1944.3557', 'aut_centralizer_order': 1296, 'aut_label': '648.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.a1.a1', 'complements': ['3.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.g1.a1', '216.h1.a1', '216.i1.a1', '324.b1.a1'], 'contains': ['1944.a1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6423, 2918, 5388, 4883, 3753, 3709, 5957, 3433], 'generators': [24], 'label': '1944.3557.648.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.b1.a1', 'normal_contained_in': ['216.a1.a1', '216.b1.a1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.b1.a1', 'projective_image': '1944.3557', 'quotient_action_image': '2.1', 'quotient_action_kernel': '324.113', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649232
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.187', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5451, 5904, 6839, 3140, 4032, 7134, 5191, 7187], 'generators': [12, 648, 24, 720, 864], 'label': '1944.3557.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649233
{'ambient': '1944.3557', 'aut_centralizer_order': 1296, 'aut_label': '648.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.a1.b1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.b1', '216.b1.a1', '216.g1.b1', '216.h1.b1', '216.i1.b1', '324.b1.b1'], 'contains': ['1944.a1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6423, 2918, 5556, 5726, 3753, 3709, 5713, 2591], 'generators': [8], 'label': '1944.3557.648.b1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.b1.b1', 'normal_contained_in': ['216.a1.b1', '216.b1.a1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.b1.b1', 'projective_image': '1944.3557', 'quotient_action_image': '2.1', 'quotient_action_kernel': '324.113', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '648.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649234
{'ambient': '1944.3557', 'aut_centralizer_order': 1296, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.g1.b1', '216.j1.a1', '216.j1.a2', '216.k1.a1', '216.k1.a2', '216.l1.a1', '324.c1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5697, -1, 5153, -1, 3317, -1, 6569, -1], 'generators': [672], 'label': '1944.3557.648.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '648.c1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649235
{'ambient': '1944.3557', 'aut_centralizer_order': 1296, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '2.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.b1', '216.g1.a1', '216.j1.b1', '216.j1.b2', '216.k1.b1', '216.k1.b2', '216.l1.a1', '324.c1.b1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5697, -1, 4751, -1, 3317, -1, 6324, -1], 'generators': [656], 'label': '1944.3557.648.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '648.c1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649236
{'ambient': '1944.3557', 'aut_centralizer_order': 1296, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '216.c1.a1', '216.l1.a1', '216.m1.a1', '216.m1.b1', '216.n1.a1', '216.n1.b1', '324.d1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4245, -1, 4852, -1, 3535, -1, 7303, -1], 'generators': [32], 'label': '1944.3557.648.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '648.d1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649237
{'ambient': '1944.3557', 'aut_centralizer_order': 648, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '216.g1.a1', '216.g1.b1', '216.l1.a1', '216.o1.a1', '216.o1.a2', '216.o1.b1', '216.o1.b2', '216.p1.a1', '216.p1.a2', '216.p1.b1', '216.p1.b2', '324.e1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4024, -1, 3828, -1, 3099, -1, 7058, -1], 'generators': [680], 'label': '1944.3557.648.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '648.e1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649238
{'ambient': '1944.3557', 'aut_centralizer_order': 216, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '216.h1.a1', '216.h1.b1', '216.j1.a1', '216.j1.a2', '216.j1.b1', '216.j1.b2', '216.m1.a1', '216.m1.b1', '216.o1.a1', '216.o1.a2', '216.o1.b1', '216.o1.b2', '324.f1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3520, -1, 4365, -1, 2866, -1, 6814, -1], 'generators': [72], 'label': '1944.3557.648.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '648.f1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649239
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '216.h1.a1', '216.i1.b1', '216.j1.a1', '216.j1.a2', '216.k1.b1', '216.k1.b2', '216.n1.a1', '216.n1.b1', '216.p1.a1', '216.p1.a2', '216.p1.b1', '216.p1.b2'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2749, -1, 2855, -1, 2091, -1, 7922, -1], 'generators': [96], 'label': '1944.3557.648.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '648.g1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649240
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.b1', '216.h1.b1', '216.i1.a1', '216.j1.b1', '216.j1.b2', '216.k1.a1', '216.k1.a2', '216.n1.a1', '216.n1.b1', '216.p1.a1', '216.p1.a2', '216.p1.b1', '216.p1.b2'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2749, -1, 2537, -1, 2091, -1, 7800, -1], 'generators': [80], 'label': '1944.3557.648.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '648.g1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649241
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '216.i1.a1', '216.i1.b1', '216.k1.a1', '216.k1.a2', '216.k1.b1', '216.k1.b2', '216.m1.a1', '216.n1.a1', '216.o1.a1', '216.o1.a2', '216.p1.a1', '216.p1.a2'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1932, -1, 2184, -1, 1867, -1, 8144, -1], 'generators': [1544], 'label': '1944.3557.648.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '648.h1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649242
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.b1', '216.i1.a1', '216.i1.b1', '216.k1.a1', '216.k1.a2', '216.k1.b1', '216.k1.b2', '216.m1.b1', '216.n1.b1', '216.o1.b1', '216.o1.b2', '216.p1.b1', '216.p1.b2'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1932, -1, 3224, -1, 1867, -1, 8032, -1], 'generators': [104], 'label': '1944.3557.648.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '648.h1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649243
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.187', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.b1', '6.b1.b1', '6.c1.b1'], 'contains': ['24.a1.b1', '36.a1.a1', '36.c1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5451, 5904, 7004, 7667, 4032, 7134, 4698, 5000], 'generators': [12, 648, 8, 720, 864], 'label': '1944.3557.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.a1.a1', '6.a1.b1'], 'normal_contains': ['24.a1.b1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649244
{'ambient': '1944.3557', 'aut_centralizer_order': 576, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '324.b1.a1', '324.b1.b1', '324.c1.a1', '324.c1.b1', '324.d1.a1', '324.e1.a1', '324.f1.a1', '486.a1.a1', '486.a1.b1', '486.b1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7034, -1, 7561, -1, 5818, -1, 3454, -1], 'generators': [12], 'label': '1944.3557.972.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '972.a1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649245
{'ambient': '1944.3557', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '648.b1.a1', '648.b1.b1', '648.c1.a1', '648.c1.b1', '648.d1.a1', '648.e1.a1', '648.f1.a1', '648.g1.a1', '648.g1.b1', '648.h1.a1', '648.h1.b1', '972.a1.a1'], 'contains': [], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4024, 3625, 4365, 4883, 3099, 4368, 7058, 3433], 'generators': [], 'label': '1944.3557.1944.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1.a1', 'normal_contained_in': ['648.a1.a1', '648.b1.a1', '648.b1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1944.a1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 107649246
{'ambient': '1944.3557', 'aut_centralizer_order': 3, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '864.4687', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.b1', '6.b1.a1', '18.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7915, 7868, 8449, 8298, 5367, 7335, 2161, 1702], 'generators': [1, 1512, 1800, 24, 648, 12, 8], 'label': '1944.3557.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
id: 107649247
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 108, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['24.c1.a1', '36.b1.a1', '36.c1.a1', '36.c1.b1', '36.d1.a1', '36.d1.b1', '36.e1.a1', '36.e1.a2', '36.e1.b1', '36.e1.b2', '36.f1.a1', '36.g1.a1', '36.g1.a2', '36.g1.a3', '36.g1.a4'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5862, -1, 7524, -1, 4553, -1, 4442, -1], 'generators': [12, 720, 8, 24, 648], 'label': '1944.3557.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '12.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649248
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 18, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.a1'], 'contains': ['24.e1.a1', '36.a1.a1', '36.d1.a1', '36.d1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4665, -1, 4681, -1, 3136, -1, 6561, -1], 'generators': [12, 648, 32, 720, 864], 'label': '1944.3557.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.c1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 107649249
{'ambient': '1944.3557', 'aut_centralizer_order': 12, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '54.a1.a1', '54.b1.b1', '54.e1.b1', '54.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8920, -1, 9001, -1, 7066, -1, 994, -1], 'generators': [1, 8, 24, 648, 12], 'label': '1944.3557.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649250
{'ambient': '1944.3557', 'aut_centralizer_order': 12, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '9.a1.a1'], 'contains': ['36.b1.a1', '54.a1.b1', '54.b1.a1', '54.e1.a1', '54.f1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8920, -1, 8767, -1, 7066, -1, 2132, -1], 'generators': [6, 24, 8, 648, 12], 'label': '1944.3557.18.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649251
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '54.c1.a1', '54.c1.b1', '54.d1.a1', '54.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8290, -1, 8567, -1, 7750, -1, 3236, -1], 'generators': [3, 24, 648, 12, 8], 'label': '1944.3557.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 107649252
{'ambient': '1944.3557', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.41', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.b1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '162.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7440, -1, 8111, -1, 5412, -1, 2477, -1], 'generators': [1, 648, 12, 1800, 1512], 'label': '1944.3557.18.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649253
{'ambient': '1944.3557', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.41', 'aut_weyl_index': 72, 'centralizer': '216.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.b1', '9.b1.a1'], 'contains': ['36.a1.a1', '162.a1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7440, -1, 6951, -1, 5412, -1, 2932, -1], 'generators': [6, 648, 12, 288, 1512], 'label': '1944.3557.18.c1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '18.c1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649308
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.b1', '24.d1.a1', '24.d1.b1'], 'contains': ['216.d1.a1', '216.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [790, -1, 1122, -1, 828, -1, 9100, -1], 'generators': [1536, 72], 'label': '1944.3557.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '648.729', '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': '9.2'}
id: 107649254
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.c1.b1', '6.d1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '162.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6987, -1, 7078, -1, 6563, -1, 4944, -1], 'generators': [3, 648, 12, 720, 1512], 'label': '1944.3557.18.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.d1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649255
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.187', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': ['81.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1975, 3959, 1714, 1842, 2018, 4789, 8189, 5398], 'generators': [24, 72, 1512], 'label': '1944.3557.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['72.b1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '648.729', 'quotient_action_image': '8.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649256
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.187', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': ['81.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.b1'], 'contains': ['72.b1.a1', '72.c1.b1', '72.g1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1975, 3959, 3188, 5000, 2018, 4789, 7901, 3140], 'generators': [8, 72, 1512], 'label': '1944.3557.24.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['8.a1.a1', '12.a1.b1'], 'normal_contains': ['72.b1.a1', '216.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '648.729', 'quotient_action_image': '8.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649257
{'ambient': '1944.3557', 'aut_centralizer_order': 3, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '864.4687', 'aut_weyl_index': 6, 'centralizer': '216.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.b1.b1', '18.a1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7915, 7868, 7490, 1702, 5367, 7335, 3323, 8298], 'generators': [6, 1512, 288, 8, 648, 12, 24], 'label': '1944.3557.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
id: 107649258
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.13', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.g1.b1', '72.h1.a1', '72.h1.b1', '72.i1.a1', '72.i1.a2', '72.i1.b1', '72.i1.b2', '72.i2.a1', '72.i2.a2'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [972, -1, 705, -1, 849, -1, 9345, -1], 'generators': [1520, 24, 72], 'label': '1944.3557.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649259
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.13', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['72.c1.b1', '72.d1.b1', '72.g1.a1', '72.h1.a1', '72.h1.b1', '72.i1.a1', '72.i1.a2', '72.i1.b1', '72.i1.b2', '72.i2.a1', '72.i2.a2'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [972, -1, 386, -1, 849, -1, 9633, -1], 'generators': [8, 1536, 72], 'label': '1944.3557.24.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.b1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649260
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 108, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1'], 'contains': ['72.a1.a1', '72.c1.a1', '72.c1.b1', '72.d1.a1', '72.d1.b1', '72.e1.a1', '72.e1.b1', '72.f1.a1', '72.f1.b1', '72.j1.a1', '72.j1.a2', '72.j1.b1', '72.j1.b2', '72.k1.a1', '72.l1.a1', '72.l1.a2', '72.l1.a3', '72.l1.a4'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2595, -1, 3878, -1, 2436, -1, 7679, -1], 'generators': [8, 24, 72, 648], 'label': '1944.3557.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649261
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['72.e1.b1', '72.f1.a1', '72.f1.b1', '72.g1.a1', '72.g1.b1', '72.h1.a1', '72.i1.b1', '72.i1.b2', '72.i2.a1', '72.i2.a2'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [510, -1, 1175, -1, 265, -1, 8769, -1], 'generators': [1088, 1536, 72], 'label': '1944.3557.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649262
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['72.e1.a1', '72.f1.a1', '72.f1.b1', '72.g1.a1', '72.g1.b1', '72.h1.b1', '72.i1.a1', '72.i1.a2', '72.i2.a1', '72.i2.a2'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [510, -1, 973, -1, 265, -1, 9057, -1], 'generators': [1520, 1536, 72], 'label': '1944.3557.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649263
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 18, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1'], 'contains': ['72.b1.a1', '72.e1.a1', '72.e1.b1', '72.h1.a1', '72.h1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1513, -1, 1543, -1, 1434, -1, 8477, -1], 'generators': [32, 72, 1512], 'label': '1944.3557.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.e1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 107649264
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '9.a1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '81.a1.a1', '81.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8386, -1, 8878, -1, 8289, -1, 1807, -1], 'generators': [1, 24, 6, 648, 12], 'label': '1944.3557.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649265
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.b1', '9.a1.a1'], 'contains': ['54.a1.b1', '54.b1.b1', '54.c1.b1', '81.a1.a1', '81.b1.b1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [8386, -1, 8368, -1, 8289, -1, 1503, -1], 'generators': [1, 8, 6, 648, 12], 'label': '1944.3557.27.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.b1', 'old_label': '27.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649266
{'ambient': '1944.3557', 'aut_centralizer_order': 2, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.889', 'aut_weyl_index': 18, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['54.f1.a1', '54.f1.b1', '54.g1.a1', '81.b1.a1', '81.b1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9936, -1, 9819, -1, 9076, -1, 1288, -1], 'generators': [1, 24, 6, 12, 8], 'label': '1944.3557.27.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.b1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 107649267
{'ambient': '1944.3557', 'aut_centralizer_order': 36, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.a1.b1', '12.c1.a1', '18.c1.a1', '18.c1.b1', '18.d1.a1'], 'contains': ['72.b1.a1', '108.f1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4346, 6180, 3401, 3340, 2730, 7592, 6878, 7187], 'generators': [12, 720, 864, 648], 'label': '1944.3557.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.a1.b1'], 'normal_contains': ['72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649268
{'ambient': '1944.3557', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '5184.qp', 'aut_weyl_index': 1, 'centralizer': '648.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '6.c1.b1', '6.d1.a1', '18.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6616, 2329, 7783, 5000, 6221, 2170, 3778, 5000], 'generators': [3, 1512, 720, 12, 648, 8, 24], 'label': '1944.3557.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '648.729'}
id: 107649269
{'ambient': '1944.3557', 'aut_centralizer_order': 72, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 648, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.a1', '18.a1.b1', '18.b1.a1'], 'contains': ['72.a1.a1', '108.a1.a1', '108.a1.b1', '108.b1.a1', '108.c1.a1', '108.c1.b1', '108.d1.a1', '108.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7311, -1, 8512, -1, 5500, -1, 3651, -1], 'generators': [12, 8, 24, 648], 'label': '1944.3557.36.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 107649270
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1'], 'contains': ['72.c1.a1', '108.a1.a1', '108.f1.a1', '108.g1.a1', '108.h1.a1', '108.h1.a2'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5451, -1, 7542, -1, 4080, -1, 5282, -1], 'generators': [12, 24, 648, 720], 'label': '1944.3557.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.c1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649271
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.b1.a1'], 'contains': ['72.c1.b1', '108.a1.b1', '108.f1.a1', '108.g1.b1', '108.h1.b1', '108.h1.b2'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5451, -1, 6524, -1, 4080, -1, 3885, -1], 'generators': [12, 8, 648, 720], 'label': '1944.3557.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.c1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649272
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1'], 'contains': ['72.e1.a1', '108.b1.a1', '108.f1.a1', '108.i1.a1', '108.j1.a1', '108.j1.a2'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4665, -1, 5319, -1, 3136, -1, 6445, -1], 'generators': [12, 32, 648, 864], 'label': '1944.3557.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.d1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649273
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1'], 'contains': ['72.e1.b1', '108.b1.a1', '108.f1.a1', '108.i1.b1', '108.j1.b1', '108.j1.b2'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4665, -1, 5587, -1, 3136, -1, 6678, -1], 'generators': [12, 32, 648, 720], 'label': '1944.3557.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.d1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649274
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.j1.a1', '108.c1.a1', '108.g1.a1', '108.h1.b1', '108.j1.a1', '108.j1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5038, -1, 6077, -1, 4553, -1, 4583, -1], 'generators': [12, 656, 24, 720], 'label': '1944.3557.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.e1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649275
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.j1.a2', '108.c1.a1', '108.g1.a1', '108.h1.b2', '108.j1.a2', '108.j1.b2'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5038, -1, 5939, -1, 4553, -1, 4118, -1], 'generators': [12, 1304, 24, 720], 'label': '1944.3557.36.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.e1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649276
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.j1.b1', '108.c1.b1', '108.g1.b1', '108.h1.a1', '108.j1.a1', '108.j1.b2'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5038, -1, 7263, -1, 4553, -1, 4816, -1], 'generators': [12, 8, 1320, 720], 'label': '1944.3557.36.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.e1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649277
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.j1.b2', '108.c1.b1', '108.g1.b1', '108.h1.a2', '108.j1.a2', '108.j1.b1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5038, -1, 7124, -1, 4553, -1, 4351, -1], 'generators': [12, 8, 672, 720], 'label': '1944.3557.36.e1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.e1.b2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649278
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 108, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.k1.a1', '108.d1.a1', '108.g1.a1', '108.g1.b1', '108.i1.a1', '108.i1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6213, -1, 7400, -1, 5025, -1, 5049, -1], 'generators': [12, 8, 24, 720], 'label': '1944.3557.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.f1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649279
{'ambient': '1944.3557', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.742', 'aut_weyl_index': 12, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '9.b1.a1', '27.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7502, -1, 7970, -1, 6963, -1, 2917, -1], 'generators': [1, 1512, 72, 6, 648, 12, 24], 'label': '1944.3557.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
id: 107649280
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.l1.a1', '108.e1.a1', '108.h1.a1', '108.h1.b1', '108.i1.b1', '108.j1.a2'], 'core': '1944.a1.a1', 'coset_action_label': '36T2997', 'count': 12, 'diagramx': [5831, -1, 6242, -1, 3608, -1, 5747, -1], 'generators': [12, 656, 1320, 720], 'label': '1944.3557.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.g1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649281
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.l1.a2', '108.e1.a1', '108.h1.a1', '108.h1.b2', '108.i1.a1', '108.j1.b1'], 'core': '1944.a1.a1', 'coset_action_label': '36T2997', 'count': 12, 'diagramx': [5831, -1, 6987, -1, 3608, -1, 5514, -1], 'generators': [12, 1304, 1320, 720], 'label': '1944.3557.36.g1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.g1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649282
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.l1.a3', '108.e1.a1', '108.h1.a2', '108.h1.b1', '108.i1.a1', '108.j1.b2'], 'core': '1944.a1.a1', 'coset_action_label': '36T2997', 'count': 12, 'diagramx': [5831, -1, 6710, -1, 3608, -1, 6212, -1], 'generators': [12, 656, 672, 720], 'label': '1944.3557.36.g1.a3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.g1.a3', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a3', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649283
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.l1.a4', '108.e1.a1', '108.h1.a2', '108.h1.b2', '108.i1.b1', '108.j1.a1'], 'core': '1944.a1.a1', 'coset_action_label': '36T2997', 'count': 12, 'diagramx': [5831, -1, 6847, -1, 3608, -1, 5980, -1], 'generators': [12, 1304, 672, 720], 'label': '1944.3557.36.g1.a4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.g1.a4', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a4', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649284
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '18.a1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '162.a1.a1', '162.c1.a1', '162.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8386, -1, 9303, -1, 7617, -1, 994, -1], 'generators': [1, 24, 648, 12], 'label': '1944.3557.54.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '648.729', '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': '2.1'}
id: 107649285
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '54.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '18.a1.b1', '27.a1.b1'], 'contains': ['108.a1.b1', '162.a1.b1', '162.c1.b1', '162.f1.b1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [8386, -1, 8368, -1, 7617, -1, 1886, -1], 'generators': [6, 8, 648, 12], 'label': '1944.3557.54.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.b1', 'old_label': '54.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649286
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '18.a1.b1', '27.a1.a1'], 'contains': ['108.a1.a1', '162.a1.b1', '162.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8780, -1, 8830, -1, 7117, -1, 2132, -1], 'generators': [6, 648, 12, 24], 'label': '1944.3557.54.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '648.729', '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': '12.4'}
id: 107649287
{'ambient': '1944.3557', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '18.a1.a1', '27.a1.b1'], 'contains': ['108.a1.b1', '162.a1.a1', '162.d1.b1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8780, -1, 8682, -1, 7117, -1, 609, -1], 'generators': [1, 648, 12, 8], 'label': '1944.3557.54.b1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649288
{'ambient': '1944.3557', 'aut_centralizer_order': 8, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '18.b1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '162.b1.a1', '162.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7901, -1, 8976, -1, 8232, -1, 3105, -1], 'generators': [3, 648, 12, 24], 'label': '1944.3557.54.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '648.729', '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': '12.4'}
id: 107649289
{'ambient': '1944.3557', 'aut_centralizer_order': 8, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '18.b1.a1', '27.a1.b1'], 'contains': ['108.a1.b1', '162.b1.a1', '162.e1.b1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [7901, -1, 8189, -1, 8232, -1, 2856, -1], 'generators': [3, 648, 12, 8], 'label': '1944.3557.54.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.b1', 'old_label': '54.c1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649290
{'ambient': '1944.3557', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.742', 'aut_weyl_index': 12, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.b1', '6.b1.b1', '6.c1.b1', '9.b1.a1', '27.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7502, -1, 8177, -1, 6963, -1, 2567, -1], 'generators': [1, 1512, 72, 6, 648, 12, 8], 'label': '1944.3557.3.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '3.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.b1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
id: 107649291
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '18.b1.a1'], 'contains': ['108.b1.a1', '162.b1.a1', '162.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6688, -1, 7908, -1, 6106, -1, 3409, -1], 'generators': [3, 648, 12, 32], 'label': '1944.3557.54.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': '648.729', '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: 107649292
{'ambient': '1944.3557', 'aut_centralizer_order': 12, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1'], 'contains': ['108.c1.a1', '162.d1.a1', '162.f1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9449, -1, 9157, -1, 6612, -1, 2382, -1], 'generators': [6, 656, 12, 24], 'label': '1944.3557.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '54.e1.a1', 'projective_image': '1944.3557', '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': '6.1'}
id: 107649293
{'ambient': '1944.3557', 'aut_centralizer_order': 12, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1'], 'contains': ['108.c1.b1', '162.d1.b1', '162.f1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9449, -1, 9696, -1, 6612, -1, 111, -1], 'generators': [1, 672, 12, 8], 'label': '1944.3557.54.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '54.e1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649294
{'ambient': '1944.3557', 'aut_centralizer_order': 12, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '27.b1.a1'], 'contains': ['108.d1.a1', '162.c1.a1', '162.d1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9936, -1, 9977, -1, 8737, -1, 360, -1], 'generators': [1, 24, 12, 8], 'label': '1944.3557.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.f1.a1', 'projective_image': '1944.3557', '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': '12.4'}
id: 107649295
{'ambient': '1944.3557', 'aut_centralizer_order': 12, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '108.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '27.b1.a1'], 'contains': ['108.d1.a1', '162.c1.b1', '162.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9936, -1, 9449, -1, 8737, -1, 1640, -1], 'generators': [6, 8, 12, 24], 'label': '1944.3557.54.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.f1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649296
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '27.b1.a1'], 'contains': ['108.d1.a1', '162.e1.a1', '162.e1.b1', '162.g1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9114, -1, 9573, -1, 9161, -1, 2647, -1], 'generators': [3, 12, 8, 24], 'label': '1944.3557.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.g1.a1', 'projective_image': '1944.3557', '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': '36.10'}
id: 107649297
{'ambient': '1944.3557', 'aut_centralizer_order': 648, 'aut_label': '72.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 648, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.b1.a1'], 'contains': ['216.a1.a1', '216.a1.b1', '216.b1.a1', '216.c1.a1', '216.g1.a1', '216.g1.b1', '216.l1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6454, 2132, 6188, 5831, 3017, 2976, 6691, 2485], 'generators': [8, 24, 648], 'label': '1944.3557.72.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['216.a1.a1', '216.a1.b1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '648.729', 'quotient_action_image': '4.2', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 107649298
{'ambient': '1944.3557', 'aut_centralizer_order': 36, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': ['27.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.a1.b1', '24.e1.a1', '36.a1.a1'], 'contains': ['216.d1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1695, 4922, 1542, 3340, 1543, 5577, 8396, 5327], 'generators': [72, 1512], 'label': '1944.3557.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.a1.a1', '24.a1.b1', '36.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '648.729', 'quotient_action_image': '8.4', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649299
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.c1.a1'], 'contains': ['216.a1.a1', '216.d1.a1', '216.e1.a1', '216.h1.a1', '216.j1.a1', '216.j1.a2'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1967, -1, 4785, -1, 2024, -1, 7548, -1], 'generators': [24, 72, 648], 'label': '1944.3557.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '648.729', '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': '6.1'}
id: 107649300
{'ambient': '1944.3557', 'aut_centralizer_order': 54, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.b1.b1', '24.c1.a1', '36.c1.b1'], 'contains': ['216.a1.b1', '216.d1.a1', '216.e1.b1', '216.h1.b1', '216.j1.b1', '216.j1.b2'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1967, -1, 5194, -1, 2024, -1, 6814, -1], 'generators': [8, 72, 648], 'label': '1944.3557.72.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.c1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649301
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '576.8300', 'aut_weyl_index': 9, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.b1.a1', '12.c1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5566, 4568, 7050, 5000, 4050, 3288, 4574, 5000], 'generators': [12, 648, 864, 8, 24, 720], 'label': '1944.3557.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 107649302
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1'], 'contains': ['216.a1.a1', '216.e1.b1', '216.f1.a1', '216.f1.b1', '216.i1.a1', '216.k1.a1', '216.k1.a2'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [975, -1, 1208, -1, 1310, -1, 8511, -1], 'generators': [80, 24, 648], 'label': '1944.3557.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '648.729', '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': '3.1'}
id: 107649303
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '24.c1.a1'], 'contains': ['216.a1.b1', '216.e1.a1', '216.f1.a1', '216.f1.b1', '216.i1.b1', '216.k1.b1', '216.k1.b2'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [975, -1, 1610, -1, 1310, -1, 8878, -1], 'generators': [8, 96, 648], 'label': '1944.3557.72.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.d1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 107649304
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.b1', '24.e1.a1', '36.d1.a1'], 'contains': ['216.c1.a1', '216.d1.a1', '216.f1.a1', '216.m1.a1', '216.o1.a1', '216.o1.a2'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2164, -1, 2148, -1, 1776, -1, 8159, -1], 'generators': [32, 1512, 648], 'label': '1944.3557.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649305
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.e1.a1', '36.d1.b1'], 'contains': ['216.c1.a1', '216.d1.a1', '216.f1.b1', '216.m1.b1', '216.o1.b1', '216.o1.b2'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2164, -1, 2382, -1, 1776, -1, 8281, -1], 'generators': [32, 72, 648], 'label': '1944.3557.72.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.e1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 107649306
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.d1.b1'], 'contains': ['216.c1.a1', '216.e1.a1', '216.e1.b1', '216.f1.a1', '216.n1.a1', '216.p1.a1', '216.p1.a2'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1425, -1, 1443, -1, 1061, -1, 8756, -1], 'generators': [800, 96, 648], 'label': '1944.3557.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '648.729', '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': '3.1'}
id: 107649307
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.d1.b1'], 'contains': ['216.c1.a1', '216.e1.a1', '216.e1.b1', '216.f1.b1', '216.n1.b1', '216.p1.b1', '216.p1.b2'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1425, -1, 1684, -1, 1061, -1, 8634, -1], 'generators': [80, 96, 648], 'label': '1944.3557.72.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.f1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 107649309
{'ambient': '1944.3557', 'aut_centralizer_order': 18, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '18.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.b1.a1', '24.d1.a1', '24.d1.b1'], 'contains': ['216.d1.a1', '216.e1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [790, -1, 1040, -1, 828, -1, 8993, -1], 'generators': [1520, 72], 'label': '1944.3557.72.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.g1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649310
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.a1', '24.e1.a1'], 'contains': ['216.d1.a1', '216.f1.a1', '216.f1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [518, -1, 906, -1, 610, -1, 9208, -1], 'generators': [1616, 1512], 'label': '1944.3557.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '648.729', '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': '9.2'}
id: 107649311
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.b1', '24.e1.a1'], 'contains': ['216.d1.a1', '216.f1.a1', '216.f1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [518, -1, 805, -1, 610, -1, 9315, -1], 'generators': [1544, 72], 'label': '1944.3557.72.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.h1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649312
{'ambient': '1944.3557', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.742', 'aut_weyl_index': 12, 'centralizer': '216.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.c1.b1', '54.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7175, 7868, 7291, 1854, 4728, 7335, 3330, 7936], 'generators': [6, 648, 1512, 12, 24, 288], 'label': '1944.3557.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.b1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '648.729', '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': '216.161'}
id: 107649313
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '18.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.b1'], 'contains': ['216.e1.a1', '216.e1.b1', '216.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [64, -1, 23, -1, 392, -1, 9852, -1], 'generators': [1520, 96], 'label': '1944.3557.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '648.729', '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': '9.2'}
id: 107649314
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '18.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.b1'], 'contains': ['216.e1.a1', '216.e1.b1', '216.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [64, -1, 95, -1, 392, -1, 9960, -1], 'generators': [1880, 96], 'label': '1944.3557.72.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.i1.a2', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649315
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '18.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.a1'], 'contains': ['216.e1.a1', '216.e1.b1', '216.f1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [64, -1, 520, -1, 392, -1, 9745, -1], 'generators': [1592, 96], 'label': '1944.3557.72.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.i1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649316
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '18.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.a1'], 'contains': ['216.e1.a1', '216.e1.b1', '216.f1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [64, -1, 430, -1, 392, -1, 9638, -1], 'generators': [1088, 96], 'label': '1944.3557.72.i1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.i1.b2', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.b2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649317
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '72.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.a1', '24.d1.b1'], 'contains': ['216.e1.a1', '216.e1.b1', '216.f1.a1', '216.f1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [246, -1, 185, -1, 174, -1, 9423, -1], 'generators': [368, 96], 'label': '1944.3557.72.i2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.i2.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i2.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649318
{'ambient': '1944.3557', 'aut_centralizer_order': 9, 'aut_label': '72.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.b1.b1', '24.d1.a1', '24.d1.b1'], 'contains': ['216.e1.a1', '216.e1.b1', '216.f1.a1', '216.f1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [246, -1, 302, -1, 174, -1, 9530, -1], 'generators': [1160, 96], 'label': '1944.3557.72.i2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.i2.a2', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i2.a2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 107649319
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.e1.a1'], 'contains': ['216.g1.a1', '216.h1.a1', '216.i1.a1', '216.j1.b1', '216.k1.b1', '216.o1.a1', '216.o1.b1', '216.p1.a1', '216.p1.b1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2696, -1, 2787, -1, 2521, -1, 7181, -1], 'generators': [656, 24, 72], 'label': '1944.3557.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.j1.a1', 'projective_image': '1944.3557', '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': '2.1'}
id: 107649320
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.e1.a2'], 'contains': ['216.g1.a1', '216.h1.a1', '216.i1.a1', '216.j1.b2', '216.k1.b2', '216.o1.a2', '216.o1.b2', '216.p1.a2', '216.p1.b2'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2696, -1, 2715, -1, 2521, -1, 6936, -1], 'generators': [1304, 24, 72], 'label': '1944.3557.72.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.j1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649321
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.e1.b1'], 'contains': ['216.g1.b1', '216.h1.b1', '216.i1.b1', '216.j1.a1', '216.k1.a1', '216.o1.a1', '216.o1.b2', '216.p1.a2', '216.p1.b1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2696, -1, 4228, -1, 2521, -1, 7303, -1], 'generators': [8, 1320, 72], 'label': '1944.3557.72.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.j1.b1', 'projective_image': '1944.3557', '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': '2.1'}
id: 107649322
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.e1.b2'], 'contains': ['216.g1.b1', '216.h1.b1', '216.i1.b1', '216.j1.a2', '216.k1.a2', '216.o1.a2', '216.o1.b1', '216.p1.a1', '216.p1.b2'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2696, -1, 3962, -1, 2521, -1, 7058, -1], 'generators': [8, 672, 72], 'label': '1944.3557.72.j1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.j1.b2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649323
{'ambient': '1944.3557', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '432.742', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.b1'], 'contains': ['12.a1.b1', '18.c1.a1', '54.b1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7175, 7868, 8363, 8159, 4728, 7335, 2083, 2064], 'generators': [1, 648, 1512, 12, 8, 1800], 'label': '1944.3557.6.a1.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
id: 107649324
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 324, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.f1.a1'], 'contains': ['216.b1.a1', '216.h1.a1', '216.h1.b1', '216.i1.a1', '216.i1.b1', '216.m1.a1', '216.m1.b1', '216.n1.a1', '216.n1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3694, -1, 5067, -1, 2769, -1, 7425, -1], 'generators': [8, 24, 72], 'label': '1944.3557.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.k1.a1', 'projective_image': '1944.3557', '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': '2.1'}
id: 107649325
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.g1.a1'], 'contains': ['216.j1.a1', '216.j1.b1', '216.k1.a1', '216.k1.b1', '216.l1.a1', '216.m1.b1', '216.n1.a1', '216.o1.a2', '216.p1.b2'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3240, -1, 3235, -1, 2273, -1, 7792, -1], 'generators': [656, 1320, 72], 'label': '1944.3557.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.l1.a1', 'projective_image': '1944.3557', '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': '2.1'}
id: 107649326
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.g1.a2'], 'contains': ['216.j1.a1', '216.j1.b2', '216.k1.a1', '216.k1.b2', '216.l1.a1', '216.m1.a1', '216.n1.b1', '216.o1.b1', '216.p1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3240, -1, 4697, -1, 2273, -1, 7670, -1], 'generators': [1304, 1320, 72], 'label': '1944.3557.72.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.l1.a2', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649327
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.g1.a3'], 'contains': ['216.j1.a2', '216.j1.b1', '216.k1.a2', '216.k1.b1', '216.l1.a1', '216.m1.a1', '216.n1.b1', '216.o1.b2', '216.p1.a2'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3240, -1, 3308, -1, 2273, -1, 8037, -1], 'generators': [656, 672, 72], 'label': '1944.3557.72.l1.a3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.l1.a3', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649328
{'ambient': '1944.3557', 'aut_centralizer_order': 27, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.g1.a4'], 'contains': ['216.j1.a2', '216.j1.b2', '216.k1.a2', '216.k1.b2', '216.l1.a1', '216.m1.b1', '216.n1.a1', '216.o1.a1', '216.p1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3240, -1, 3859, -1, 2273, -1, 7915, -1], 'generators': [1304, 672, 72], 'label': '1944.3557.72.l1.a4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.l1.a4', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a4', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649329
{'ambient': '1944.3557', 'aut_centralizer_order': 8, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 648, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '27.a1.a1', '27.a1.b1'], 'contains': ['162.a1.a1', '162.a1.b1', '162.b1.a1', '243.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8388, -1, 8366, -1, 9540, -1, 1357, -1], 'generators': [1, 6, 648, 12], 'label': '1944.3557.81.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '648.729', '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: 107649330
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1'], 'contains': ['162.c1.a1', '162.d1.a1', '162.e1.a1', '243.a1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9933, -1, 9541, -1, 9888, -1, 1185, -1], 'generators': [1, 6, 12, 24], 'label': '1944.3557.81.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '81.b1.a1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649331
{'ambient': '1944.3557', 'aut_centralizer_order': 4, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.b1', '27.b1.a1'], 'contains': ['162.c1.b1', '162.d1.b1', '162.e1.b1', '243.a1.a1'], 'core': '648.b1.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [9933, -1, 9676, -1, 9888, -1, 803, -1], 'generators': [1, 6, 12, 8], 'label': '1944.3557.81.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.b1', 'old_label': '81.b1.b1', 'projective_image': '1944.3557', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 107649332
{'ambient': '1944.3557', 'aut_centralizer_order': 144, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'contains': ['216.a1.a1', '324.a1.a1', '324.b1.a1', '324.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7784, -1, 8548, -1, 6630, -1, 3096, -1], 'generators': [12, 24, 648], 'label': '1944.3557.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 107649333
{'ambient': '1944.3557', 'aut_centralizer_order': 144, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.b1', '54.a1.b1', '54.b1.b1', '54.c1.b1'], 'contains': ['216.a1.b1', '324.a1.a1', '324.b1.b1', '324.c1.b1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7784, -1, 7852, -1, 6630, -1, 2893, -1], 'generators': [12, 8, 648], 'label': '1944.3557.108.a1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.a1.b1', 'projective_image': '648.729', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}

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.