Formats: - HTML - YAML - JSON - 2026-07-25T08:05:04.806314
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [8, 6], 'aut_gens': [[31912822053969032426664959351243617259375, 52878688246952082101717061182872151690757], [96037484558798779197801630916813522237414, 265918190277008586096336390098395831585674], [170189502706641977002422219240156131394603, 64119510370652666556023368596285583063677]], 'aut_group': '93312.it', 'aut_hash': 1575027877360827811, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 93312, 'aut_permdeg': 180, 'aut_perms': [27214680338051205395926898987492081399490401746489277843535152463614398455673581358148864922874834219005325464904543157437204783616539300658540418328331497452163174604115854485716935636332942200768691330093279040435956271545467741763450029090822548983835883041648500300734945886543777523071930078359251944584922683484847537313463, 197650467249421232307215673984571960911931254316710858895717446128726531354292097721204889978957783822234997547005663192132158596698070228112192874690879082606435123885709077759373991113591788056456552737403645719634238076934049363931409949720216705805126641781779707854413422373032470685962451149143961170583217273541544388278822], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 81, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [3, 24, 1, 2], [3, 32, 1, 1], [3, 72, 2, 1], [3, 144, 2, 1], [3, 288, 1, 1], [3, 288, 2, 1], [3, 576, 1, 1], [3, 576, 2, 1], [4, 972, 1, 1], [4, 1944, 1, 1], [6, 216, 1, 1], [6, 288, 1, 1], [6, 432, 1, 1], [6, 648, 1, 3], [6, 648, 2, 1], [6, 1296, 2, 3], [6, 2592, 1, 1], [6, 2592, 2, 1], [9, 864, 2, 1], [9, 1728, 1, 1], [12, 3888, 1, 1], [12, 3888, 2, 1], [18, 2592, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:\\GOrthPlus(4,3)', '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': 72, 'autcentquo_group': '93312.it', 'autcentquo_hash': 1575027877360827811, 'autcentquo_nilpotent': False, 'autcentquo_order': 93312, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:\\GOrthPlus(4,3)', 'cc_stats': [[1, 1, 1], [2, 36, 1], [2, 81, 1], [2, 162, 1], [2, 324, 1], [3, 24, 2], [3, 32, 1], [3, 72, 2], [3, 144, 2], [3, 288, 3], [3, 576, 3], [4, 972, 1], [4, 1944, 1], [6, 216, 1], [6, 288, 1], [6, 432, 1], [6, 648, 5], [6, 1296, 6], [6, 2592, 3], [9, 864, 2], [9, 1728, 1], [12, 3888, 3], [18, 2592, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '46656.ja', 'commutator_count': 1, 'commutator_label': '7776.bc', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 235, 'cyclic': False, 'derived_length': 5, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 81, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [3, 24, 1, 2], [3, 32, 1, 1], [3, 72, 2, 1], [3, 144, 2, 1], [3, 288, 1, 1], [3, 288, 2, 1], [3, 576, 1, 1], [3, 576, 2, 1], [4, 972, 1, 1], [4, 1944, 1, 1], [6, 216, 1, 1], [6, 288, 1, 1], [6, 432, 1, 1], [6, 648, 1, 3], [6, 648, 2, 1], [6, 1296, 2, 3], [6, 2592, 1, 1], [6, 2592, 2, 1], [9, 864, 2, 1], [9, 1728, 1, 1], [12, 3888, 1, 1], [12, 3888, 2, 1], [18, 2592, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 9600, 'exponent': 36, 'exponents_of_order': [6, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 4], [24, 1, 4], [32, 0, 4], [32, 1, 2], [48, 1, 1], [64, 0, 2], [64, 1, 1], [72, 1, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '46656.ja', 'hash': 5818217150007363221, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [6, 12], 'inner_gens': [[31912822053969032426664959351243617259375, 159558940328320778330223643849308790236721], [191473383790593053302913656633974294552387, 52878688246952082101717061182872151690757]], 'inner_hash': 5818217150007363221, 'inner_nilpotent': False, 'inner_order': 46656, 'inner_split': True, 'inner_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'inner_used': [1, 2], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 6], [2, 3], [4, 6], [6, 3], [8, 3], [9, 2], [24, 8], [32, 6], [48, 1], [64, 3], [72, 4]], 'label': '46656.ja', 'linC_count': 8, 'linC_degree': 24, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 4, 'linQ_dim': 24, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 24, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C3^4:Omega+(4,3):C2', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 33, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 45, 'number_divisions': 33, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 563, 'number_subgroup_classes': 576, 'number_subgroups': 173030, 'old_label': None, 'order': 46656, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 603], [3, 3104], [4, 2916], [6, 19728], [9, 3456], [12, 11664], [18, 5184]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[137977917219016197287271761825829384836972, 223384312881112699829713650451011876090483]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 9, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 3], [6, 1], [8, 3], [9, 2], [12, 1], [16, 1], [24, 4], [32, 2], [48, 3], [64, 3], [72, 4], [128, 1]], 'representations': {'PC': {'code': '1780400336176241085605688345909204954850699547405481360287648401713817418879062289229701733858613854194998411831239046613799215181463787260881661763625276864560256145648831235325100630641274818365996514724209141514217752070516740085328656740476973934068353702568007126792090984341981287951', 'gens': [1, 3, 4, 5, 6, 8, 10, 11, 12], 'pres': [12, 2, 3, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 24, 882362, 688622, 159866, 446691, 1085631, 152379, 46119, 1270084, 163636, 75448, 90400, 368069, 846953, 316037, 23945, 209, 3592518, 997938, 18174, 84042, 4380487, 864883, 436927, 63019, 82615, 17347, 28687, 283, 4354568, 725792, 6956, 77816, 28580, 944, 4008969, 725781, 529953, 11577, 61509, 2961, 7293, 2965258, 1140502, 735010, 304174, 73978, 38086, 9586, 4846, 4396043, 2363927, 608291, 76091, 72647, 31187, 15647]}, 'Perm': {'d': 36, 'gens': [31912822053969032426664959351243617259375, 52878688246952082101717061182872151690757]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:\\OmegaPlus(4,3):C_2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 162664270
      {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 235, 'group_order': 46656, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 162664281
      {'aut_label': '2A', 'centralizer': '36.c1.a1', 'counter': 2, 'group_counter': 235, 'group_order': 46656, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 3531009747471662219011299102392565362, 'size': 36}
    • id: 162664292
      {'aut_label': '2B', 'centralizer': '81.a1.a1', 'counter': 3, 'group_counter': 235, 'group_order': 46656, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 295767292394709819554907672945973848506, 'size': 81}
    • id: 162664303
      {'aut_label': '2C', 'centralizer': '162.a1.a1', 'counter': 4, 'group_counter': 235, 'group_order': 46656, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 297832378730548408612909819638652870456469, 'size': 162}
    • id: 162664310
      {'aut_label': '2D', 'centralizer': '324.c1.a1', 'counter': 5, 'group_counter': 235, 'group_order': 46656, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 20964796601880266709516209741170238195784, 'size': 324}
    • id: 162664311
      {'aut_label': '3A', 'centralizer': '24.b1.a1', 'counter': 6, 'group_counter': 235, 'group_order': 46656, 'label': '3A', 'order': 3, 'powers': [6, 1], 'representative': 271362822238261510988783673098960787, 'size': 24}
    • id: 162664312
      {'aut_label': '3B', 'centralizer': '24.c1.a1', 'counter': 7, 'group_counter': 235, 'group_order': 46656, 'label': '3B', 'order': 3, 'powers': [7, 1], 'representative': 418802676036117422539392240, 'size': 24}
    • id: 162664313
      {'aut_label': '3C', 'centralizer': '32.a1.a1', 'counter': 8, 'group_counter': 235, 'group_order': 46656, 'label': '3C', 'order': 3, 'powers': [8, 1], 'representative': 10628907036247073378848273409681764461604, 'size': 32}
    • id: 162664314
      {'aut_label': '3D1', 'centralizer': '72.i1.a1', 'counter': 9, 'group_counter': 235, 'group_order': 46656, 'label': '3D1', 'order': 3, 'powers': [10, 1], 'representative': 223677916168037849352608221605095685412319, 'size': 72}
    • id: 162664271
      {'aut_label': '3D1', 'centralizer': '72.i1.a1', 'counter': 10, 'group_counter': 235, 'group_order': 46656, 'label': '3D-1', 'order': 3, 'powers': [9, 1], 'representative': 265625665105588355303028484565815564951201, 'size': 72}
    • id: 162664272
      {'aut_label': '3E1', 'centralizer': '144.g1.a1', 'counter': 11, 'group_counter': 235, 'group_order': 46656, 'label': '3E1', 'order': 3, 'powers': [12, 1], 'representative': 297541220379964272269131624234872858069144, 'size': 144}
    • id: 162664273
      {'aut_label': '3E1', 'centralizer': '144.g1.a1', 'counter': 12, 'group_counter': 235, 'group_order': 46656, 'label': '3E-1', 'order': 3, 'powers': [11, 1], 'representative': 191765645831182207704709872854360330179224, 'size': 144}
    • id: 162664274
      {'aut_label': '3F', 'centralizer': '288.l1.a1', 'counter': 13, 'group_counter': 235, 'group_order': 46656, 'label': '3F', 'order': 3, 'powers': [13, 1], 'representative': 137981447862475908986897362260447680409844, 'size': 288}
    • id: 162664275
      {'aut_label': '3G1', 'centralizer': '288.v1.a1', 'counter': 14, 'group_counter': 235, 'group_order': 46656, 'label': '3G1', 'order': 3, 'powers': [15, 1], 'representative': 116699994885176602136221668510589635962883, 'size': 288}
    • id: 162664276
      {'aut_label': '3G1', 'centralizer': '288.v1.a1', 'counter': 15, 'group_counter': 235, 'group_order': 46656, 'label': '3G-1', 'order': 3, 'powers': [14, 1], 'representative': 287208064173357884993887086911383166818295, 'size': 288}
    • id: 162664277
      {'aut_label': '3H', 'centralizer': '576.q1.a1', 'counter': 16, 'group_counter': 235, 'group_order': 46656, 'label': '3H', 'order': 3, 'powers': [16, 1], 'representative': 340080496568034991034200403813359281527012, 'size': 576}
    • id: 162664278
      {'aut_label': '3I1', 'centralizer': '576.t1.a1', 'counter': 17, 'group_counter': 235, 'group_order': 46656, 'label': '3I1', 'order': 3, 'powers': [18, 1], 'representative': 180521564380149322790462904546120762607924, 'size': 576}
    • id: 162664279
      {'aut_label': '3I1', 'centralizer': '576.t1.a1', 'counter': 18, 'group_counter': 235, 'group_order': 46656, 'label': '3I-1', 'order': 3, 'powers': [17, 1], 'representative': 319118704696551950799589504176279732224634, 'size': 576}
    • id: 162664280
      {'aut_label': '4A', 'centralizer': '972.e1.a1', 'counter': 19, 'group_counter': 235, 'group_order': 46656, 'label': '4A', 'order': 4, 'powers': [3, 19], 'representative': 287208064173365016050637542515042137939389, 'size': 972}
    • id: 162664282
      {'aut_label': '4B', 'centralizer': '1944.t1.a1', 'counter': 20, 'group_counter': 235, 'group_order': 46656, 'label': '4B', 'order': 4, 'powers': [4, 20], 'representative': 42251393819567534189229943034828904575754, 'size': 1944}
    • id: 162664283
      {'aut_label': '6A', 'centralizer': '216.h1.a1', 'counter': 21, 'group_counter': 235, 'group_order': 46656, 'label': '6A', 'order': 6, 'powers': [6, 2], 'representative': 3259646925233427684283272386188117829, 'size': 216}
    • id: 162664284
      {'aut_label': '6B', 'centralizer': '288.b1.a1', 'counter': 22, 'group_counter': 235, 'group_order': 46656, 'label': '6B', 'order': 6, 'powers': [8, 2], 'representative': 74156355553122189832560920018345737394518, 'size': 288}
    • id: 162664285
      {'aut_label': '6C', 'centralizer': '432.m1.a1', 'counter': 23, 'group_counter': 235, 'group_order': 46656, 'label': '6C', 'order': 6, 'powers': [7, 2], 'representative': 74156355553122608608253517941196135521970, 'size': 432}
    • id: 162664286
      {'aut_label': '6D', 'centralizer': '648.c1.a1', 'counter': 24, 'group_counter': 235, 'group_order': 46656, 'label': '6D', 'order': 6, 'powers': [7, 4], 'representative': 297832378730548020832661290534327361195765, 'size': 648}
    • id: 162664287
      {'aut_label': '6E', 'centralizer': '648.i1.a1', 'counter': 25, 'group_counter': 235, 'group_order': 46656, 'label': '6E', 'order': 6, 'powers': [6, 4], 'representative': 287204524209113002941979034388840654638642, 'size': 648}
    • id: 162664288
      {'aut_label': '6F', 'centralizer': '648.d1.a1', 'counter': 26, 'group_counter': 235, 'group_order': 46656, 'label': '6F', 'order': 6, 'powers': [6, 5], 'representative': 361652573713613190395131952594345347540557, 'size': 648}
    • id: 162664289
      {'aut_label': '6G1', 'centralizer': '648.n1.a1', 'counter': 27, 'group_counter': 235, 'group_order': 46656, 'label': '6G1', 'order': 6, 'powers': [9, 3], 'representative': 265920363411273272619544260816749013592444, 'size': 648}
    • id: 162664290
      {'aut_label': '6G1', 'centralizer': '648.n1.a1', 'counter': 28, 'group_counter': 235, 'group_order': 46656, 'label': '6G-1', 'order': 6, 'powers': [10, 3], 'representative': 223382946490992594791566633311749194953477, 'size': 648}
    • id: 162664291
      {'aut_label': '6H1', 'centralizer': '1296.j1.a1', 'counter': 29, 'group_counter': 235, 'group_order': 46656, 'label': '6H1', 'order': 6, 'powers': [11, 5], 'representative': 202101764546874249283487772484488599567280, 'size': 1296}
    • id: 162664293
      {'aut_label': '6H1', 'centralizer': '1296.j1.a1', 'counter': 30, 'group_counter': 235, 'group_order': 46656, 'label': '6H-1', 'order': 6, 'powers': [12, 5], 'representative': 307868655970966491372720847636221805987194, 'size': 1296}
    • id: 162664294
      {'aut_label': '6I1', 'centralizer': '1296.i1.a1', 'counter': 31, 'group_counter': 235, 'group_order': 46656, 'label': '6I1', 'order': 6, 'powers': [12, 3], 'representative': 10336119063663061325257397654129643617133, 'size': 1296}
    • id: 162664295
      {'aut_label': '6I1', 'centralizer': '1296.i1.a1', 'counter': 32, 'group_counter': 235, 'group_order': 46656, 'label': '6I-1', 'order': 6, 'powers': [11, 3], 'representative': 10338300402779198895296350083976213546175, 'size': 1296}
    • id: 162664296
      {'aut_label': '6J1', 'centralizer': '1296.a1.a1', 'counter': 33, 'group_counter': 235, 'group_order': 46656, 'label': '6J1', 'order': 6, 'powers': [12, 2], 'representative': 275963176088373729628708452321670127133602, 'size': 1296}
    • id: 162664297
      {'aut_label': '6J1', 'centralizer': '1296.a1.a1', 'counter': 34, 'group_counter': 235, 'group_order': 46656, 'label': '6J-1', 'order': 6, 'powers': [11, 2], 'representative': 275959627920222163132671282983379889253789, 'size': 1296}
    • id: 162664298
      {'aut_label': '6K', 'centralizer': '2592.n1.a1', 'counter': 35, 'group_counter': 235, 'group_order': 46656, 'label': '6K', 'order': 6, 'powers': [13, 3], 'representative': 276257594030636346810759889991547460686722, 'size': 2592}
    • id: 162664299
      {'aut_label': '6L1', 'centralizer': '2592.be1.a1', 'counter': 36, 'group_counter': 235, 'group_order': 46656, 'label': '6L1', 'order': 6, 'powers': [14, 5], 'representative': 297542289952436603435827481431670178176066, 'size': 2592}
    • id: 162664300
      {'aut_label': '6L1', 'centralizer': '2592.be1.a1', 'counter': 37, 'group_counter': 235, 'group_order': 46656, 'label': '6L-1', 'order': 6, 'powers': [15, 5], 'representative': 106363858817547151395044535482820791472716, 'size': 2592}
    • id: 162664301
      {'aut_label': '9A1', 'centralizer': '864.g1.a1', 'counter': 38, 'group_counter': 235, 'group_order': 46656, 'label': '9A1', 'order': 9, 'powers': [39, 8], 'representative': 20666295941926490139332529650672047296146, 'size': 864}
    • id: 162664302
      {'aut_label': '9A1', 'centralizer': '864.g1.a1', 'counter': 39, 'group_counter': 235, 'group_order': 46656, 'label': '9A-1', 'order': 9, 'powers': [38, 8], 'representative': 10628380783113870498429702352841710255291, 'size': 864}
    • id: 162664304
      {'aut_label': '9B', 'centralizer': '1728.q1.a1', 'counter': 40, 'group_counter': 235, 'group_order': 46656, 'label': '9B', 'order': 9, 'powers': [40, 8], 'representative': 371987359569999459215888062150458479387643, 'size': 1728}
    • id: 162664305
      {'aut_label': '12A', 'centralizer': '3888.s1.a1', 'counter': 41, 'group_counter': 235, 'group_order': 46656, 'label': '12A', 'order': 12, 'powers': [24, 20], 'representative': 148311328307404208824117990143387721451519, 'size': 3888}
    • id: 162664306
      {'aut_label': '12B1', 'centralizer': '3888.n1.a1', 'counter': 42, 'group_counter': 235, 'group_order': 46656, 'label': '12B1', 'order': 12, 'powers': [27, 19], 'representative': 148614717667874122839676193027213139279214, 'size': 3888}
    • id: 162664307
      {'aut_label': '12B1', 'centralizer': '3888.n1.a1', 'counter': 43, 'group_counter': 235, 'group_order': 46656, 'label': '12B-1', 'order': 12, 'powers': [28, 19], 'representative': 84788513931041827843496726159968957193974, 'size': 3888}
    • id: 162664308
      {'aut_label': '18A1', 'centralizer': '2592.e1.a1', 'counter': 44, 'group_counter': 235, 'group_order': 46656, 'label': '18A1', 'order': 18, 'powers': [38, 22], 'representative': 64118440394925686788367037667173104264158, 'size': 2592}
    • id: 162664309
      {'aut_label': '18A1', 'centralizer': '2592.e1.a1', 'counter': 45, 'group_counter': 235, 'group_order': 46656, 'label': '18A-1', 'order': 18, 'powers': [39, 22], 'representative': 84784736310018630623465369530877851846321, 'size': 2592}
  • gps_qchar • Show schema
    • id: 16164082
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.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], 'schur_index': 1}
    • id: 16164093
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.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], 'schur_index': 1}
    • id: 16164104
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1], 'schur_index': 1}
    • id: 16164109
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -2, -2, -2, -2, 2, 2, -2, -1, -1, 1, 1, -1, -1, 1, 1, 2, 1, 1, -1, -1, 2, -2, -1, -1, 1, 1], 'schur_index': 1}
    • id: 16164110
      {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 0, 2, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, 2, 0, 0, 0, 0, 2, 2, 0, -1, -1, 0, 0, 2, 2, 0, 0, -1, 0, 0, 2, 2, -1, 0, -1, -1, 0, 0], 'schur_index': 1}
    • id: 16164111
      {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.2b', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 0, 4, 4, 0, 4, 4, 4, 1, 1, -2, -2, -2, -2, -2, -2, 1, 1, 4, 0, 0, 0, 0, 4, 4, 0, 1, 1, 0, 0, -2, -2, 0, 0, -2, 0, 0, -2, -2, -2, 0, 1, 1, 0, 0], 'schur_index': 1}
    • id: 16164112
      {'cdim': 4, 'counter': 7, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.4a', 'multiplicity': 1, 'nt': [24, 1482], 'qdim': 4, 'qvalues': [4, -2, -4, 0, 2, 4, 4, 4, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, -2, -2, -2, 0, 0, 2, 2, 2, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 1, 1], 'schur_index': 1}
    • id: 16164113
      {'cdim': 4, 'counter': 8, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.4b', 'multiplicity': 1, 'nt': [24, 1482], 'qdim': 4, 'qvalues': [4, 2, -4, 0, -2, 4, 4, 4, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, 2, 2, 2, 0, 0, -2, 2, 2, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 0, 0, 0, -1, -1], 'schur_index': 1}
    • id: 16164084
      {'cdim': 6, 'counter': 11, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.6a', 'multiplicity': 1, 'nt': [8, 42], 'qdim': 6, 'qvalues': [6, 0, 6, -2, 0, 6, 6, 6, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 2, 0, 0, 0, 0, -2, -2, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
    • id: 16164114
      {'cdim': 4, 'counter': 9, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.4c', 'multiplicity': 2, 'nt': [24, 1483], 'qdim': 8, 'qvalues': [8, -4, -8, 0, 4, 8, 8, 8, 2, 2, -1, -1, 2, -1, -1, 2, 2, 2, 0, 0, -4, -4, -4, 0, 0, 4, -2, -2, 1, 1, 1, 1, -1, -1, -2, 1, 1, -1, -1, 2, 0, 0, 0, -1, -1], 'schur_index': 1}
    • id: 16164083
      {'cdim': 4, 'counter': 10, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.4d', 'multiplicity': 2, 'nt': [24, 1483], 'qdim': 8, 'qvalues': [8, 4, -8, 0, -4, 8, 8, 8, 2, 2, -1, -1, 2, -1, -1, 2, 2, 2, 0, 0, 4, 4, 4, 0, 0, -4, -2, -2, -1, -1, 1, 1, 1, 1, -2, -1, -1, -1, -1, 2, 0, 0, 0, 1, 1], 'schur_index': 1}
    • id: 16164086
      {'cdim': 8, 'counter': 13, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.8a', 'multiplicity': 1, 'nt': [24, 1482], 'qdim': 8, 'qvalues': [8, 0, -8, 0, 0, 8, 8, 8, 2, 2, 2, 2, -1, 2, 2, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, -2, 0, 0, 1, 0, 0, 2, 2, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164088
      {'cdim': 9, 'counter': 15, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.9a', 'multiplicity': 1, 'nt': [12, 128], 'qdim': 9, 'qvalues': [9, 3, 9, 1, 3, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -1, 3, 3, 3, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164089
      {'cdim': 9, 'counter': 16, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.9b', 'multiplicity': 1, 'nt': [18, 112], 'qdim': 9, 'qvalues': [9, -3, 9, 1, -3, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, -3, -3, -3, 1, 1, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164085
      {'cdim': 6, 'counter': 12, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.6b', 'multiplicity': 2, 'nt': [24, 702], 'qdim': 12, 'qvalues': [12, 0, 12, -4, 0, 12, 12, 12, -3, -3, 0, 0, 0, 0, 0, 0, -3, -3, 4, 0, 0, 0, 0, -4, -4, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
    • id: 16164087
      {'cdim': 8, 'counter': 14, 'faithful': False, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.8b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 16, 'qvalues': [16, 0, -16, 0, 0, 16, 16, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164090
      {'cdim': 24, 'counter': 17, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.24a', 'multiplicity': 1, 'nt': [36, 16176], 'qdim': 24, 'qvalues': [24, 6, 0, 4, 2, -3, 6, -3, 0, 0, 6, 6, 0, -3, -3, 0, 0, 0, 0, 0, 3, -3, 0, -2, 1, -1, 0, 0, 2, 2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164091
      {'cdim': 24, 'counter': 18, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.24b', 'multiplicity': 1, 'nt': [36, 16177], 'qdim': 24, 'qvalues': [24, 12, 0, 4, 0, 6, -3, -3, 0, 0, 0, 0, 6, 0, 0, -3, 0, 0, 0, 2, 0, 3, -3, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164092
      {'cdim': 24, 'counter': 19, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.24c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -12, 0, 4, 0, 6, -3, -3, 0, 0, 0, 0, 6, 0, 0, -3, 0, 0, 0, -2, 0, -3, 3, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164094
      {'cdim': 24, 'counter': 20, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.24d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -6, 0, 4, -2, -3, 6, -3, 0, 0, 6, 6, 0, -3, -3, 0, 0, 0, 0, 0, -3, 3, 0, -2, 1, 1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164097
      {'cdim': 32, 'counter': 23, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.32a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 8, 0, 0, 0, -4, -4, 5, 8, 8, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1], 'schur_index': 1}
    • id: 16164098
      {'cdim': 32, 'counter': 24, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.32b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 32, 'qvalues': [32, -8, 0, 0, 0, -4, -4, 5, 8, 8, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -1, -1, -1, 0, 0, 0, 1, 1], 'schur_index': 1}
    • id: 16164095
      {'cdim': 24, 'counter': 21, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.24e', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 12, 0, 8, 4, -6, 12, -6, 0, 0, -6, -6, 0, 3, 3, 0, 0, 0, 0, 0, 6, -6, 0, -4, 2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164096
      {'cdim': 24, 'counter': 22, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.24f', 'multiplicity': 2, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, -12, 0, 8, -4, -6, 12, -6, 0, 0, -6, -6, 0, 3, 3, 0, 0, 0, 0, 0, -6, 6, 0, -4, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164101
      {'cdim': 48, 'counter': 27, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.48a', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 8, 0, 12, -6, -6, 0, 0, 0, 0, -6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164099
      {'cdim': 32, 'counter': 25, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.32c', 'multiplicity': 2, 'nt': [96, 0], 'qdim': 64, 'qvalues': [64, 16, 0, 0, 0, -8, -8, 10, -8, -8, -2, -2, 4, -2, -2, 4, 1, 1, 0, 0, -8, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 1, 1, -2, 0, 0, 0, 1, 1], 'schur_index': 1}
    • id: 16164100
      {'cdim': 32, 'counter': 26, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.32d', 'multiplicity': 2, 'nt': [192, 0], 'qdim': 64, 'qvalues': [64, -16, 0, 0, 0, -8, -8, 10, -8, -8, -2, -2, 4, -2, -2, 4, 1, 1, 0, 0, 8, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, -2, 0, 0, 0, -1, -1], 'schur_index': 1}
    • id: 16164102
      {'cdim': 64, 'counter': 28, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.64a', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 64, 'qvalues': [64, 0, 0, 0, 0, -8, -8, 10, -8, -8, 4, 4, -2, 4, 4, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164105
      {'cdim': 72, 'counter': 30, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.72a', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 72, 'qvalues': [72, -6, 0, -4, 6, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 2, -1, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164106
      {'cdim': 72, 'counter': 31, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.72b', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 72, 'qvalues': [72, 12, 0, -4, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, -3, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164107
      {'cdim': 72, 'counter': 32, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.72c', 'multiplicity': 1, 'nt': [216, 0], 'qdim': 72, 'qvalues': [72, -12, 0, -4, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 3, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164108
      {'cdim': 72, 'counter': 33, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.72d', 'multiplicity': 1, 'nt': [216, 0], 'qdim': 72, 'qvalues': [72, 6, 0, -4, -6, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 2, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16164103
      {'cdim': 64, 'counter': 29, 'faithful': True, 'group': '46656.ja', 'group_order': 46656, 'image': None, 'label': '46656.ja.64b', 'multiplicity': 2, 'nt': [192, 0], 'qdim': 128, 'qvalues': [128, 0, 0, 0, 0, -16, -16, 20, 8, 8, -4, -4, -4, -4, -4, -4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
    • id: 36250175
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 46656, 'label': '46656.ja.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]]]}
    • id: 36250186
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 23328, 'label': '46656.ja.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]]]}
    • id: 36250197
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 15552, 'label': '46656.ja.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
    • id: 36250208
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 15552, 'label': '46656.ja.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
    • id: 36250215
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 7776, 'label': '46656.ja.1d1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]]]}
    • id: 36250216
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 7776, 'label': '46656.ja.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]]]}
    • id: 36250217
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 7776, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 7776, 'label': '46656.ja.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250218
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 7776, 'counter': 8, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 2592, 'label': '46656.ja.2b1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
    • id: 36250219
      {'center': '6.a1.a1', 'center_index': 6, 'center_order': 7776, 'counter': 9, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 2592, 'label': '46656.ja.2b2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
    • id: 36250176
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 10, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.4a', 'nt': [24, 1482], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
    • id: 36250177
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 11, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.4b', 'nt': [24, 1482], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 36250178
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 12, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.4c1', 'nt': [24, 1483], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]]]}
    • id: 36250179
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 13, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.4c2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]]]}
    • id: 36250180
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 14, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.4d1', 'nt': [24, 1483], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]]]}
    • id: 36250181
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 15, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.4d2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]]]}
    • id: 36250182
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 16, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '288.1025', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 162, 'label': '46656.ja.6a', 'nt': [8, 42], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250183
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 17, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '288.1025', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 162, 'label': '46656.ja.6b1', 'nt': [24, 702], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
    • id: 36250184
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 18, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '288.1025', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 162, 'label': '46656.ja.6b2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
    • id: 36250185
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 19, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.8a', 'nt': [24, 1482], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250187
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 20, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.8b1', 'nt': [72, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250188
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 21, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '576.8277', 'image_order': 576, 'indicator': 0, 'kernel': '576.a1.a1', 'kernel_order': 81, 'label': '46656.ja.8b2', 'nt': [72, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250189
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 22, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '288.1025', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 162, 'label': '46656.ja.9a', 'nt': [12, 128], 'q_character': None, 'values': [[[9, 0]], [[3, 0]], [[9, 0]], [[1, 0]], [[3, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250190
      {'center': '288.a1.a1', 'center_index': 288, 'center_order': 162, 'counter': 23, 'cyclotomic_n': 1, 'dim': 9, 'faithful': False, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '288.1025', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 162, 'label': '46656.ja.9b', 'nt': [18, 112], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, 0]], [[1, 0]], [[-3, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250191
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.24a', 'nt': [36, 16176], 'q_character': None, 'values': [[[24, 0]], [[6, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250192
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.24b', 'nt': [36, 16177], 'q_character': None, 'values': [[[24, 0]], [[12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[1, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250193
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.24c', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[1, 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]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250194
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.24d', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-6, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250195
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.24e1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[6, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250196
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.24e2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[6, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250198
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.24f1', 'nt': [144, 0], 'q_character': None, 'values': [[[24, 0]], [[-6, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250199
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.24f2', 'nt': [144, 2], 'q_character': None, 'values': [[[24, 0]], [[-6, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250200
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.32a', 'nt': [48, 0], 'q_character': None, 'values': [[[32, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 36250201
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.32b', 'nt': [72, 0], 'q_character': None, 'values': [[[32, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
    • id: 36250202
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 3, 'dim': 32, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.32c1', 'nt': [96, 0], 'q_character': None, 'values': [[[32, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[8, -1]], [[8, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]]]}
    • id: 36250203
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 3, 'dim': 32, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.32c2', 'nt': [96, 2], 'q_character': None, 'values': [[[32, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[8, 1]], [[8, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]]]}
    • id: 36250204
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 3, 'dim': 32, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.32d1', 'nt': [192, 0], 'q_character': None, 'values': [[[32, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[8, -1]], [[8, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]]]}
    • id: 36250205
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 3, 'dim': 32, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.32d2', 'nt': [192, 2], 'q_character': None, 'values': [[[32, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[5, 0]], [[8, 1]], [[8, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]]]}
    • id: 36250206
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.48a', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250207
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 1, 'dim': 64, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.64a', 'nt': [96, 0], 'q_character': None, 'values': [[[64, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[10, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250209
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 3, 'dim': 64, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.64b1', 'nt': [192, 0], 'q_character': None, 'values': [[[64, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[10, 0]], [[-8, 1]], [[-8, -1]], [[4, 1]], [[4, -1]], [[-2, 0]], [[4, 1]], [[4, -1]], [[-2, 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]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250210
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 3, 'dim': 64, 'faithful': True, 'field': [1, -1, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 0, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.64b2', 'nt': [192, 2], 'q_character': None, 'values': [[[64, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[10, 0]], [[-8, -1]], [[-8, 1]], [[4, -1]], [[4, 1]], [[-2, 0]], [[4, -1]], [[4, 1]], [[-2, 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]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250211
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 1, 'dim': 72, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.72a', 'nt': [144, 0], 'q_character': None, 'values': [[[72, 0]], [[-6, 0]], [[0, 0]], [[-4, 0]], [[6, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250212
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 1, 'dim': 72, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.72b', 'nt': [144, 0], 'q_character': None, 'values': [[[72, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-1, 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]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250213
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 1, 'dim': 72, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.72c', 'nt': [216, 0], 'q_character': None, 'values': [[[72, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[-1, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36250214
      {'center': '46656.a1.a1', 'center_index': 46656, 'center_order': 1, 'counter': 45, 'cyclotomic_n': 1, 'dim': 72, 'faithful': True, 'field': [0, 1], 'group': '46656.ja', 'group_counter': 235, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ja', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1.a1', 'kernel_order': 1, 'label': '46656.ja.72d', 'nt': [216, 0], 'q_character': None, 'values': [[[72, 0]], [[6, 0]], [[0, 0]], [[-4, 0]], [[-6, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • gps_subgroup_search • Show schema
    Showing the first 100 of 576 matching records in this table.
    • id: 216733397
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 46656, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '46656.ja.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': '46656.ja', 'subgroup_hash': 5818217150007363221, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'supersolvable': False, 'sylow': 0}
    • id: 216733508
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 23328, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ja.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '23328.je', 'subgroup_hash': 4637251834960896659, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:\\OmegaPlus(4,3)', 'supersolvable': False, 'sylow': 0}
    • id: 216733619
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 15552, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ja.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15552.t', 'subgroup_hash': 1617233341634141621, 'subgroup_order': 15552, 'subgroup_tex': 'C_3:S_3^3:S_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733730
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 7776, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15552.s', 'subgroup_hash': 5186829056886078061, 'subgroup_order': 15552, 'subgroup_tex': 'S_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733841
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 7776, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ja.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '7776.bc', 'subgroup_hash': 6195886690473434947, 'subgroup_order': 7776, 'subgroup_tex': 'C_3:S_3^3:A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733929
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 7776, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ja.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7776.bc', 'subgroup_hash': 6195886690473434947, 'subgroup_order': 7776, 'subgroup_tex': 'C_3:S_3^3:A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733940
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.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': '7776.iq', 'subgroup_hash': 5457175150437015127, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
    • id: 216733951
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.el', 'subgroup_hash': 3686938360739699673, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^4:(C_3\\times \\SL(2,3))', 'supersolvable': False, 'sylow': 0}
    • id: 216733962
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.bv', 'subgroup_hash': 8028542901996450327, 'subgroup_order': 5184, 'subgroup_tex': 'S_3\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
    • id: 216733398
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.bt', 'subgroup_hash': 6945509031187788888, 'subgroup_order': 3888, 'subgroup_tex': 'S_3^4:C_3', 'supersolvable': False, 'sylow': 0}
    • id: 216733409
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '3888.bq', 'subgroup_hash': 5541825096805648039, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
    • id: 216733420
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.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': '3888.bw', 'subgroup_hash': 1308481736150857399, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
    • id: 216733431
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.16.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.gb', 'subgroup_hash': 8900406544936336986, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4:(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 216733442
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2592, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ja.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ci', 'subgroup_hash': 1359974926057248800, 'subgroup_order': 2592, 'subgroup_tex': 'C_3:S_3^3:C_2^2', 'supersolvable': False, 'sylow': 0}
    • id: 216733453
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '2592.cm', 'subgroup_hash': 6952908971992144288, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 216733464
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.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': '2592.cl', 'subgroup_hash': 4141360107334104887, 'subgroup_order': 2592, 'subgroup_tex': 'C_3:S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733475
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3882', 'subgroup_hash': 3882, 'subgroup_order': 1944, 'subgroup_tex': 'S_3\\times C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733486
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '1944.3880', 'subgroup_hash': 3880, 'subgroup_order': 1944, 'subgroup_tex': 'S_3^3:C_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 216733497
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '1944.3876', 'subgroup_hash': 3876, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr S_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733509
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3881', 'subgroup_hash': 3881, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
    • id: 216733520
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3881', 'subgroup_hash': 3881, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
    • id: 216733531
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2330', 'subgroup_hash': 2330, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 216733542
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3875', 'subgroup_hash': 3875, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
    • id: 216733553
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2295', 'subgroup_hash': 2295, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
    • id: 216733564
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2295', 'subgroup_hash': 2295, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
    • id: 216733575
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3879', 'subgroup_hash': 3879, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:S_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733586
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1180', 'subgroup_hash': 1180, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 216733597
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1182', 'subgroup_hash': 1182, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:(C_3\\times C_6)', 'supersolvable': True, 'sylow': 0}
    • id: 216733608
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1184', 'subgroup_hash': 1184, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 216733620
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733631
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3528', 'subgroup_hash': 3528, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^2:S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 216733642
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3494', 'subgroup_hash': 3494, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:C_6', 'supersolvable': False, 'sylow': 0}
    • id: 216733653
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3538', 'subgroup_hash': 3538, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 216733664
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '1296.3490', 'subgroup_hash': 3490, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
    • id: 216733675
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3537', 'subgroup_hash': 3537, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:D_4:C_2', 'supersolvable': False, 'sylow': 0}
    • id: 216733686
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3497', 'subgroup_hash': 3497, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733697
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3531', 'subgroup_hash': 3531, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:(C_2\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 216733708
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.438', 'subgroup_hash': 438, 'subgroup_order': 972, 'subgroup_tex': '\\He_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733719
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.802', 'subgroup_hash': 802, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733731
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.460', 'subgroup_hash': 460, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733742
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 216733753
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.877', 'subgroup_hash': 877, 'subgroup_order': 972, 'subgroup_tex': 'C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733764
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.877', 'subgroup_hash': 877, 'subgroup_order': 972, 'subgroup_tex': 'C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733775
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '46656.ja.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.307', 'subgroup_hash': 307, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_3^2', 'supersolvable': True, 'sylow': 3}
    • id: 216733786
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '648.706', 'subgroup_hash': 706, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733797
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 216733808
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 216733819
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733830
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
    • id: 216733842
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
    • id: 216733853
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 216733864
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '648.704', 'subgroup_hash': 704, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733875
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '648.702', 'subgroup_hash': 702, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
    • id: 216733886
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
    • id: 216733897
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
    • id: 216733908
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 216733919
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 216733927
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733928
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '648.734', 'subgroup_hash': 734, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 216733930
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.o2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o2.a1', 'outer_equivalence': False, 'perfect': False, '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': '648.734', 'subgroup_hash': 734, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 216733931
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 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': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 216733932
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '648.703', 'subgroup_hash': 703, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733933
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '648.703', 'subgroup_hash': 703, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733934
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '648.723', 'subgroup_hash': 723, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 216733935
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.81.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '576.8277', 'subgroup_hash': 8277, 'subgroup_order': 576, 'subgroup_tex': '\\OmegaPlus(4,3):C_2', 'supersolvable': False, 'sylow': 0}
    • id: 216733936
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.117', 'subgroup_hash': 117, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 216733937
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.237', 'subgroup_hash': 237, 'subgroup_order': 486, 'subgroup_tex': 'C_3^3:(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 216733938
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.130', 'subgroup_hash': 130, 'subgroup_order': 486, 'subgroup_tex': 'C_3^3.(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 216733939
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.115', 'subgroup_hash': 115, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 216733941
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.236', 'subgroup_hash': 236, 'subgroup_order': 486, 'subgroup_tex': 'C_3^3:(C_3\\times C_6)', 'supersolvable': True, 'sylow': 0}
    • id: 216733942
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.146', 'subgroup_hash': 146, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 216733943
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.167', 'subgroup_hash': 167, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 216733944
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.167', 'subgroup_hash': 167, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 216733945
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.236', 'subgroup_hash': 236, 'subgroup_order': 486, 'subgroup_tex': 'C_3^3:(C_3\\times C_6)', 'supersolvable': True, 'sylow': 0}
    • id: 216733946
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.131', 'subgroup_hash': 131, 'subgroup_order': 486, 'subgroup_tex': 'C_3^3.(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 216733947
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.116', 'subgroup_hash': 116, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 216733948
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.185', 'subgroup_hash': 185, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 216733949
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
    • id: 216733950
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 216733952
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.69', 'subgroup_hash': 69, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 216733953
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733954
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733955
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733956
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733957
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733958
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 216733959
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733960
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.39', 'subgroup_hash': 39, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 216733961
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733963
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733964
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733965
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733966
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733967
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733968
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733969
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
    • id: 216733970
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733971
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.144.r2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.r2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 216733972
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '288.889', 'subgroup_hash': 889, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 216733399
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ja', 'ambient_counter': 235, 'ambient_order': 46656, 'ambient_tex': 'C_3^4:\\OmegaPlus(4,3):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ja.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '288.860', 'subgroup_hash': 860, 'subgroup_order': 288, 'subgroup_tex': '\\OmegaPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 576 matching records in this table.
    • id: 216733397
      {'ambient': '46656.ja', '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': '46656.a1.a1', 'complements': ['46656.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '16.a1.a1', '81.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6147, 6678, 4657, 6678, 4379, 5063, 5482, 5063], 'generators': [51704033854554571437363, 4889323539096746538547753599744880709, 295241039866686163195720164433782901949, 351028004128750631605570970995860994563594, 10628380783110079692622515092497064064000, 295241039874623882848923312856951927800, 303092881675368488808440317543072183203, 8683143932971954400776961842796037695, 212430023509916876092753124992548214045915, 526279357810204189480672114507821508, 806609900825601826955984788, 106363043823389105545893585833978124276212], 'label': '46656.ja.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '46656.ja', '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': '46656.ja'}
    • id: 216733398
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.d1.a1', '36.c1.a1', '36.d1.a1', '48.a1.a1', '324.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8378, -1, 5305, -1, 8977, -1, 5126, -1], 'generators': [806609900825601826955984788, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 4889323539096746538547753599744880709, 295241039874623882848923312856951927800, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '46656.ja', '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': '3888.bt'}
    • id: 216733399
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '81.a1.a1'], 'contains': ['486.a1.a1', '486.b1.a1', '486.c1.a1', '648.n1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5494, -1, 4382, -1, 4195, -1, 5383, -1], 'generators': [116400687619376953303174549852989103549892, 295241039867073968179685254207105096442, 5415567529440094410578998843851753601, 303092881674949634430682356042965385744, 295241039874623882848923312856951927800, 212429497257389240241368171342131672128571, 371694826323195982217335767205640051251050], 'label': '46656.ja.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '46656.ja', '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': '288.1025'}
    • id: 216733400
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1'], 'contains': ['576.b1.a1', '576.e1.a1', '576.f1.a1', '576.g1.a1', '576.u1.a1', '576.w1.a1', '576.w1.a2'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2565, -1, 600, -1, 1226, -1, 557, -1], 'generators': [84489214924396471641344287155346749442685, 806609900825601826955984788, 10628907036246266795930886378956136621508, 20666295941926908942006010467684606720002, 51704033854554571437363], 'label': '46656.ja.192.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '243.37'}
    • id: 216733401
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.b1.a1', '96.e1.a1', '96.i1.a1'], 'contains': ['576.b1.a1', '576.c1.a1', '576.d1.a1', '576.j1.a1', '576.k1.a1', '576.p1.a1', '576.q1.a1', '576.t1.a1', '576.v1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2121, -1, 1883, -1, 1159, -1, 955, -1], 'generators': [7968769049307653935737638642, 806609900825601826955984788, 10628907036246266795930886378956136621508, 74450773495376451245716003266092392988186, 51704033854554571437363], 'label': '46656.ja.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
    • id: 216733402
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.j1.a1'], 'contains': ['576.c1.a1', '576.e1.a1', '576.g1.a1', '576.r1.a1', '576.s1.a1', '576.s1.a2'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2511, -1, 471, -1, 586, -1, 1407, -1], 'generators': [7968769049307653935737638642, 84489214924396471641344287155346749442685, 806609900825601826955984788, 10628907036246266795930886378956136621508, 51704033854554571437363], 'label': '46656.ja.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.c1.a1', 'old_label': '192.c1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '486.145'}
    • id: 216733403
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.c1.a1'], 'contains': ['576.d1.a1', '576.e1.a1', '576.f1.a1', '576.l1.a1', '576.m1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3397, -1, 1780, -1, 1639, -1, 1643, -1], 'generators': [806609900825601826955984788, 10628907036246266795930886378956136621508, 74450773495376451245716003266092392988186, 20666295941926908942006010467684606720002, 51704033854554571437363], 'label': '46656.ja.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.a1.a1', 'old_label': '192.d1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.a1', 'subgroup_fusion': None, 'weyl_group': '486.102'}
    • id: 216733404
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.f1.a1'], 'contains': ['576.a1.a1', '576.b1.a1', '576.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2840, -1, 2631, -1, 1403, -1, 894, -1], 'generators': [806609900825601826955984788, 526279357810204189480672114507821508, 371694571423728688104004753607444239600564, 10628380783110079692622515092497064064000, 51704033854554571437363], 'label': '46656.ja.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '192.e1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.a1', 'subgroup_fusion': None, 'weyl_group': '648.702'}
    • id: 216733405
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '64.a1.a1', '96.a1.a1', '96.g1.a1', '96.k1.a1'], 'contains': ['576.a1.a1', '576.c1.a1', '576.f1.a1', '576.h1.a1', '576.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4624, -1, 3983, -1, 4477, -1, 2902, -1], 'generators': [7968769049307653935737638642, 806609900825601826955984788, 526279357810204189480672114507821508, 10628380783110079692622515092497064064000, 51704033854554571437363], 'label': '46656.ja.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '192.f1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 216733406
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '64.a1.a1', '96.d1.a1', '96.h1.a1', '96.l1.a1'], 'contains': ['576.a1.a1', '576.d1.a1', '576.g1.a1', '576.n1.a1', '576.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4334, -1, 4746, -1, 3869, -1, 2642, -1], 'generators': [371989796008778110427505343593016279502132, 806609900825601826955984788, 526279357810204189480672114507821508, 10628380783110079692622515092497064064000, 51704033854554571437363], 'label': '46656.ja.192.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '192.g1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
    • id: 216733407
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '108.b1.a1'], 'contains': ['432.c1.a1', '432.u1.a1', '432.ba1.a1', '648.a1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8951, -1, 6257, -1, 9113, -1, 6393, -1], 'generators': [303381467301831984632523399028447236213, 526279358197957461991556476205226240, 4889323539096746538547753599744880709, 418829652053207300505680884, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203], 'label': '46656.ja.216.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '216.a1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '648.705'}
    • id: 216733408
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '108.b1.a1'], 'contains': ['432.j1.a1', '432.j1.a2', '432.l1.a1', '432.t1.a1', '432.u1.a1', '432.y1.a1', '648.a1.a1', '648.f1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8883, -1, 6615, -1, 9038, -1, 6967, -1], 'generators': [20969388832130375727973188936299340343203, 303381467301831984632523399028447236213, 526279357391426248638338447114880243, 10628380783109273084969692034465828973603, 10633541442640045908254719369691861334961, 51704033854554571437363], 'label': '46656.ja.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '216.b1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 216733409
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '24.j1.a1', '36.b1.a1', '36.e1.a1', '48.c1.a1', '324.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5370, -1, 6788, -1, 5073, -1, 5980, -1], 'generators': [180521564380141788362288626246736243603250, 106363043823389105545893585833978124276212, 806609900825601826955984788, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '12.b1.a1', 'projective_image': '46656.ja', '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': '3888.bq'}
    • id: 216733410
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '108.b1.a1'], 'contains': ['432.b1.a1', '432.c1.a1', '432.h1.a1', '432.l1.a1', '432.m1.a1', '432.r1.a1', '432.t1.a1', '648.b1.a1', '648.g1.a1', '648.h1.a1', '648.h1.a2'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [7971, -1, 7685, -1, 8143, -1, 6887, -1], 'generators': [806582924808469848094809744, 526279357391426248638338447114880243, 295241039867492770848301020249397883546, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 302566629147732612700336125538638307444], 'label': '46656.ja.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '216.c1.a1', 'projective_image': '46656.ja', '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': '216.162'}
    • id: 216733411
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '108.b1.a1'], 'contains': ['432.h1.a1', '432.j1.a1', '432.j1.a2', '432.n1.a1', '432.r1.a1', '432.u1.a1', '648.h1.a1', '648.h1.a2', '648.j1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8171, -1, 7802, -1, 8632, -1, 7007, -1], 'generators': [526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783109273084969692034465828973603, 303092881675368488808440317543072183203, 10333156198067383248291935023310637301949, 51704033854554571437363], 'label': '46656.ja.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '216.d1.a1', 'projective_image': '46656.ja', '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': '216.162'}
    • id: 216733412
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '108.a1.a1'], 'contains': ['432.i1.a1', '432.k1.a1', '432.o1.a1', '432.s1.a1', '432.v1.a1', '648.g1.a1', '648.j1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6586, -1, 8833, -1, 7013, -1, 7047, -1], 'generators': [526279357391426248638338447114880243, 295241039867492770848301020249397883546, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 51704033854554571437363], 'label': '46656.ja.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.e1.a1', 'projective_image': '46656.ja', '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': '432.741'}
    • id: 216733413
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '108.a1.a1'], 'contains': ['432.o1.a1', '432.w1.a1', '432.z1.a1', '648.l1.a1', '1944.e1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6066, -1, 8937, -1, 6392, -1, 9344, -1], 'generators': [20673637994561237793188098629985154027641, 526279357391426248638338447114880243, 106363043823389105545893585833978124276212, 10628380783109691860669709973502134890388, 8683143932971954400776961842796037695, 51704033854554571437363], 'label': '46656.ja.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.f1.a1', 'projective_image': '46656.ja', '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': '144.186'}
    • id: 216733414
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.h1.a1', '108.a1.a1'], 'contains': ['432.o1.a1', '432.x1.a1', '432.bb1.a1', '648.l1.a1', '1944.f1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5883, -1, 8606, -1, 6076, -1, 9261, -1], 'generators': [95734663040279832512627927654241339479639, 526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 7596960639770528185922250573334958762, 51704033854554571437363], 'label': '46656.ja.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '216.g1.a1', 'projective_image': '46656.ja', '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': '432.741'}
    • id: 216733415
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '108.b1.a1'], 'contains': ['432.c1.a1', '432.j1.a1', '432.j1.a2', '432.m1.a1', '432.n1.a1', '432.y1.a1', '648.i1.a1', '648.m1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8679, -1, 6384, -1, 8722, -1, 7480, -1], 'generators': [20671711517985672795603354801291953047202, 526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783109273084969692034465828973603, 303092881675368488808440317543072183203, 51704033854554571437363], 'label': '46656.ja.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '216.h1.a1', 'projective_image': '46656.ja', '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': '72.46'}
    • id: 216733416
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.f1.a1', '72.g1.a1', '108.b1.a1'], 'contains': ['432.l1.a1', '432.n1.a1', '432.ba1.a1', '648.m1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8591, -1, 6153, -1, 9188, -1, 7539, -1], 'generators': [526279358197957461991556476205226240, 8683143932971954400776961842796037695, 4889323539096746538547753599744880709, 418829652053207300505680884, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203], 'label': '46656.ja.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '216.i1.a1', 'projective_image': '46656.ja', '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': '648.705'}
    • id: 216733417
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '72.i1.a1'], 'contains': ['432.q1.a1', '648.w1.a1', '1944.p1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3817, -1, 3531, -1, 3559, -1, 4721, -1], 'generators': [106367381402988864063080083556735302637372, 308169856053392076121607332823750770414320, 10628907036247073405824291587544812057843, 351323245159463972521961075657549008027466, 20961536954955839840033584020085321871549, 526279357810177213463540390961872784], 'label': '46656.ja.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1.a1', 'old_label': '216.j1.a1', 'projective_image': '46656.ja', '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': '216.153'}
    • id: 216733418
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '72.i1.a1'], 'contains': ['648.w1.a1', '864.t1.a1', '1944.q1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3619, -1, 3399, -1, 3427, -1, 4523, -1], 'generators': [287206442608751149926550391865543936119285, 10628380783109273084969692034465828973603, 212141046534731461359761857275260497795347, 10333156198067383196587901210601652898186, 351323245159463972521961075657549008027466, 526279357810177213463540390961872784], 'label': '46656.ja.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1.a1', 'old_label': '216.k1.a1', 'projective_image': '46656.ja', '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': '216.153'}
    • id: 216733419
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '72.i1.a1'], 'contains': ['648.w1.a1', '864.v1.a1', '1944.r1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4115, -1, 3749, -1, 3681, -1, 4799, -1], 'generators': [95738474375889666408176649110165874182875, 806609900825601826955984788, 295241039866686214899754018733046360505, 295241039874623882848923312856951927800, 287503560102936681050484912905478817543920, 10628907036246266847634920191397366378384], 'label': '46656.ja.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1.a1', 'old_label': '216.l1.a1', 'projective_image': '46656.ja', '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': '216.153'}
    • id: 216733420
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.g1.a1', '36.f1.a1', '48.d1.a1', '972.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4575, -1, 4360, -1, 3730, -1, 4649, -1], 'generators': [51704033854554571437363, 351323245159463972521961075657549008027466, 295241039866686163195720164433782901949, 10628380783110079692622515092497064064000, 212141046534731461359761857275260497795347, 526279357810204189480672114507821508, 806609900825601826955984788, 106363043823389105545893585833978124276212, 212434097701941936720570190139316786096024], 'label': '46656.ja.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.c1.a1', 'projective_image': '46656.ja', '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': '7776.iq'}
    • id: 216733421
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '72.i1.a1'], 'contains': ['648.w1.a1', '864.w1.a1', '1944.s1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3674, -1, 3862, -1, 3477, -1, 4866, -1], 'generators': [106367381402988864063080083556735302637372, 20961536954955839815305568385762570942905, 271362822657064179604549715384490243, 351028004128750631605570970995860994563594, 10628907036246266795930886378956136621508, 297541475279430259957908755645277254914083], 'label': '46656.ja.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.i1.a1', 'old_label': '216.m1.a1', 'projective_image': '46656.ja', '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': '216.153'}
    • id: 216733422
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '108.a1.a1'], 'contains': ['432.s1.a1', '432.w1.a1', '432.x1.a1', '648.s1.a1', '1944.t1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6705, -1, 9076, -1, 6604, -1, 9449, -1], 'generators': [526279357391426248638338447114880243, 295241039867492770848301020249397883546, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 95739280827621191398333398617704155640915, 51704033854554571437363], 'label': '46656.ja.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.n1.a1', 'projective_image': '46656.ja', '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': '432.741'}
    • id: 216733423
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '72.o1.a1', '108.b1.a1'], 'contains': ['432.r1.a1', '432.y1.a1', '432.ba1.a1', '648.u1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8488, -1, 6499, -1, 8783, -1, 7943, -1], 'generators': [20671711517985672795603354801291953047202, 526279357391426248638338447114880243, 10628380783109273084969692034465828973603, 303092881675368488808440317543072183203, 10333156198067383248291935023310637301949, 51704033854554571437363], 'label': '46656.ja.216.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '216.o1.a1', 'projective_image': '46656.ja', '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': '648.705'}
    • id: 216733424
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '72.o2.a1', '108.a1.a1'], 'contains': ['432.s1.a1', '432.z1.a1', '432.bb1.a1', '648.v1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5943, -1, 8679, -1, 6531, -1, 8852, -1], 'generators': [302837991359806326054208756689159258480, 116400958982198772737288664322276851179491, 526279357810204189480672114507821508, 10628380783110079692622515092497064064000, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.216.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '216.p1.a1', 'projective_image': '46656.ja', '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': '1296.3490'}
    • id: 216733425
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1.a1', '108.a1.a1'], 'contains': ['432.v1.a1', '432.x1.a1', '432.z1.a1', '648.z1.a1', '1944.w1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5733, -1, 8542, -1, 6019, -1, 9206, -1], 'generators': [303381467301831984632523399028447236213, 20673637994561237793188098629985154027641, 526279357391426248638338447114880243, 10628380783109691860669709973502134890388, 116400958982199579293230033886352232538612, 51704033854554571437363], 'label': '46656.ja.216.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.q1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 216733426
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '72.r1.a1', '72.s1.a1', '108.a1.a1'], 'contains': ['432.v1.a1', '432.w1.a1', '432.bb1.a1', '648.z1.a1', '1944.z1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5578, -1, 8074, -1, 5919, -1, 9133, -1], 'generators': [303381467301831984632523399028447236213, 95734663040279832512627927654241339479639, 526279357391426248638338447114880243, 10628380783110079692622515092497064064000, 7596960639770528185922250573334958762, 51704033854554571437363], 'label': '46656.ja.216.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '216.r1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 216733427
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '81.a1.a1'], 'contains': ['486.b1.a1', '729.a1.a1', '972.b1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [8394, -1, 4972, -1, 6512, -1, 5475, -1], 'generators': [116400687619376953303174549852989103549892, 295241039867073968179685254207105096442, 5415567529440094410578998843851753601, 8683143932971954400776961842796037695, 303092881674949634430682356042965385744, 295241039874623882848923312856951927800, 212429497257389240241368171342131672128571], 'label': '46656.ja.243.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1.a1', 'old_label': '243.a1.a1', 'projective_image': '46656.ja', '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': '96.70'}
    • id: 216733428
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '243.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '81.a1.a1'], 'contains': ['486.c1.a1', '729.a1.a1', '972.c1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6877, -1, 6810, -1, 4880, -1, 6782, -1], 'generators': [95734391704287768655628053164098586071492, 191763201333154242860812354709944411857212, 4889323539515524479147132005358403442, 8683143932971954400776961842796037695, 20969388832131182335621146901770109449744, 20961536954956258669678216876260888674042, 361656911173533384218669862159109459011693], 'label': '46656.ja.243.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '243.b1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.b1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1025'}
    • id: 216733429
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '96.g1.a1', '96.h1.a1', '144.d1.a1', '144.j1.a1', '144.k1.a1'], 'contains': ['576.a1.a1', '864.x1.a1', '864.y1.a1', '864.z1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4471, 5001, 4681, 5001, 4596, 5000, 5404, 5000], 'generators': [806609900825601826955984788, 526279357810204189480672114507821508, 10628380783110079692622515092497064064000, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.288.a1.a1', 'mobius_quo': 0, 'mobius_sub': 48, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '46656.ja'}
    • id: 216733430
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '96.a1.a1', '144.a1.a1'], 'contains': ['576.h1.a1', '864.a1.a1', '864.b1.a1', '864.c1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [6425, -1, 4763, -1, 5427, -1, 4366, -1], 'generators': [806582924808469848094809744, 526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 106363298713707651554369414312181236029707], 'label': '46656.ja.288.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 216733431
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3709, -1, 3962, -1, 2890, -1, 3472, -1], 'generators': [106067802792673666786562796867287085855601, 806609900825601826955984788, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 74162314549879162585470587006814584545773, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2916.gb'}
    • id: 216733432
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '144.c1.a1'], 'contains': ['576.c1.a1', '864.b1.a1', '864.d1.a1', '864.f1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4030, -1, 3539, -1, 3028, -1, 4098, -1], 'generators': [806582924808469848094809744, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 116401213898738522940563810370348489169324], 'label': '46656.ja.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.a1.a1', 'old_label': '288.c1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 216733433
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.c1.a1'], 'contains': ['576.f1.a1', '864.c1.a1', '864.d1.a1', '864.g1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [4196, -1, 2909, -1, 3319, -1, 2999, -1], 'generators': [806582924808469848094809744, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 106363298713707651554369414312181236029707], 'label': '46656.ja.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '288.d1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.a1', 'subgroup_fusion': None, 'weyl_group': '162.35'}
    • id: 216733434
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.d1.a1', '144.d1.a1', '144.e1.a1', '144.f1.a1'], 'contains': ['576.a1.a1', '864.a1.a1', '864.d1.a1', '864.e1.a1', '864.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5101, -1, 5181, -1, 5710, -1, 5806, -1], 'generators': [806609900825601826955984788, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 51704033854554571437363], 'label': '46656.ja.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '288.e1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.190'}
    • id: 216733435
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '144.b1.a1'], 'contains': ['576.p1.a1', '864.b1.a1', '864.i1.a1', '864.j1.a1', '864.k1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1204, -1, 2512, -1, 2220, -1, 3910, -1], 'generators': [806582924808469848094809744, 8683143932971954400776961842796037695, 74162585895017876807793029685849145093197, 10628380783110079692622515092497064064000, 106362772461180822312885285175687447357464], 'label': '46656.ja.288.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.b1.a1', 'old_label': '288.f1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
    • id: 216733436
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.c1.a1', '96.d1.a1', '144.h1.a1'], 'contains': ['576.d1.a1', '864.d1.a1', '864.i1.a1', '864.l1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3146, -1, 3189, -1, 2727, -1, 4004, -1], 'generators': [806609900825601826955984788, 8683143932971954400776961842796037695, 180226866056773347083021461721293621697855, 10628380783110079692622515092497064064000, 526279357810177213463540390961872784], 'label': '46656.ja.288.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '288.g1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
    • id: 216733437
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '144.g1.a1'], 'contains': ['576.j1.a1', '864.f1.a1', '864.j1.a1', '864.k1.a1', '864.l1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1387, -1, 2594, -1, 1914, -1, 3798, -1], 'generators': [84790966668980080697792966127615821470797, 10628652119101755771614443005494173904883, 8683143932971954400776961842796037695, 526279357391401520621615883974791204, 116401213898738522940563810370348489169324], 'label': '46656.ja.288.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.b1.a1', 'old_label': '288.h1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
    • id: 216733438
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1'], 'contains': ['576.l1.a1', '864.g1.a1', '864.l1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3508, -1, 1986, -1, 2502, -1, 2549, -1], 'generators': [84790966668980080697792966127615821470797, 10628652119101755771614443005494173904883, 8683143932971954400776961842796037695, 526279357391401520621615883974791204, 95734917957428940629428795828904723389467], 'label': '46656.ja.288.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.c1.a1', 'old_label': '288.i1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
    • id: 216733439
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '96.d1.a1', '144.i1.a1'], 'contains': ['576.n1.a1', '864.h1.a1', '864.l1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4741, -1, 5649, -1, 4359, -1, 3696, -1], 'generators': [806582924808469848094809744, 10628380783109691860669709973502134890388, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 159560298770325050549561693285672192436955], 'label': '46656.ja.288.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.c1.a1', 'old_label': '288.j1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
    • id: 216733440
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '144.g1.a1'], 'contains': ['576.j1.a1', '864.m1.a1', '864.n1.a1', '864.o1.a1', '864.p1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2284, -1, 2313, -1, 2386, -1, 1983, -1], 'generators': [806609900825601826955984788, 295241039866686214899754018733046360505, 295241039874623882848923312856951927800, 10628907036246266822906903469089534016147, 74450773495376451220987986920394662649629], 'label': '46656.ja.288.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.g1.a1', 'old_label': '288.k1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
    • id: 216733441
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '144.b1.a1'], 'contains': ['576.p1.a1', '864.m1.a1', '864.q1.a1', '864.r1.a1', '864.s1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2058, -1, 2218, -1, 2021, -1, 2094, -1], 'generators': [806609900825601826955984788, 295241039874623882848923312856951927800, 74450773495376451245716003266092392988186, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.288.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.b1.a1', 'old_label': '288.l1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
    • id: 216733442
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': ['2592.l1.a1', '2592.m1.a1', '2592.bk1.a1', '2592.bl1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.h1.a1', '1458.c1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6716, 5001, 4565, 5001, 4640, 5000, 6149, 5000], 'generators': [212430023509916876092753124992548214045915, 106363043823389105545893585833978124276212, 806609900825601826955984788, 526279357810204189480672114507821508, 4889323539096746538547753599744880709, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '46656.ja', 'quotient_action_image': '18.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '46656.ja'}
    • id: 216733443
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '96.e1.a1'], 'contains': ['576.v1.a1', '864.m1.a1', '864.t1.a1', '864.u1.a1', '864.v1.a1', '864.w1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2911, -1, 2414, -1, 1807, -1, 1062, -1], 'generators': [806609900825601826955984788, 10628907036246266795930886378956136621508, 295241039866686214899754018733046360505, 295241039874623882848923312856951927800, 74450773495376451220987986920394662649629], 'label': '46656.ja.288.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.m1.a1', 'old_label': '288.m1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 216733444
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.f1.a1'], 'contains': ['576.b1.a1', '864.n1.a1', '864.q1.a1', '864.t1.a1', '864.u1.a1', '864.x1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3021, -1, 2689, -1, 1720, -1, 1145, -1], 'generators': [10628380783109691860669709973502134890388, 526279357810204189480672114507821508, 351323245159463972521961075657549008027466, 20961536954955839840033584020085321871549, 51704033854554571437363], 'label': '46656.ja.288.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.e1.a1', 'old_label': '288.n1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.a1', 'subgroup_fusion': None, 'weyl_group': '486.236'}
    • id: 216733445
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.g1.a1', '144.c1.a1'], 'contains': ['576.c1.a1', '864.o1.a1', '864.r1.a1', '864.v1.a1', '864.x1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3841, -1, 3343, -1, 2863, -1, 2431, -1], 'generators': [806609900825601826955984788, 10628907036246266795930886378956136621508, 295241039874623882848923312856951927800, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.288.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.b1.a1', 'old_label': '288.o1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.a1', 'subgroup_fusion': None, 'weyl_group': '972.802'}
    • id: 216733446
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.h1.a1', '144.h1.a1'], 'contains': ['576.d1.a1', '864.p1.a1', '864.s1.a1', '864.w1.a1', '864.x1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2785, -1, 3918, -1, 2568, -1, 2486, -1], 'generators': [271362823044819707537240744665728244, 806609900825601826955984788, 351028004128750631605570970995860994563594, 10628907036246266795930886378956136621508, 10333156198067383248291935023310637301949], 'label': '46656.ja.288.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.b1.a1', 'old_label': '288.p1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1.a1', 'subgroup_fusion': None, 'weyl_group': '972.802'}
    • id: 216733447
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '96.g1.a1', '144.a1.a1'], 'contains': ['576.h1.a1', '864.r1.a1', '864.y1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [6553, -1, 4577, -1, 5279, -1, 3611, -1], 'generators': [806609900825601826955984788, 295241039874623882848923312856951927800, 10628380783110079692622515092497064064000, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.288.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.a1.a1', 'old_label': '288.q1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.a1', 'subgroup_fusion': None, 'weyl_group': '162.11'}
    • id: 216733448
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '96.h1.a1', '144.i1.a1'], 'contains': ['576.n1.a1', '864.p1.a1', '864.z1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4682, -1, 5561, -1, 4290, -1, 3499, -1], 'generators': [351028004128750631605570970995860994563594, 526279357810204189480672114507821508, 10628380783110079692622515092497064064000, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.288.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.i1.a1', 'old_label': '288.r1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.a1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
    • id: 216733449
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '144.f1.a1', '144.j1.a1', '144.l1.a1', '144.m1.a1', '144.r1.a1', '144.r2.a1'], 'contains': ['576.a1.a1', '864.ba1.a1', '864.bb1.a1', '864.bc1.a1', '864.bd1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7140, -1, 8218, -1, 7217, -1, 8238, -1], 'generators': [806609900825601826955984788, 526279357810204189480672114507821508, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 51704033854554571437363], 'label': '46656.ja.288.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '288.s1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.a1', 'subgroup_fusion': None, 'weyl_group': '288.889'}
    • id: 216733450
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '96.j1.a1', '96.k1.a1', '144.c1.a1'], 'contains': ['576.c1.a1', '864.be1.a1', '864.bf1.a1', '864.bl1.a1', '864.bm1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1644, -1, 2827, -1, 1549, -1, 2292, -1], 'generators': [303381467301831984632523399028447236213, 806582924808469848094809744, 526279357810204189480672114507821508, 10628380783110079692622515092497064064000, 116401213898738522940563810370348489169324], 'label': '46656.ja.288.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.c1.a1', 'old_label': '288.t1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
    • id: 216733451
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '144.g1.a1'], 'contains': ['576.j1.a1', '864.be1.a1', '864.bh1.a1', '864.bn1.a1', '864.bq1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [687, -1, 2063, -1, 1316, -1, 1729, -1], 'generators': [303381467301831984632523399028447236213, 95734917957429359405126502845972292587068, 84790966668980080697792966127615821470797, 10628652119101755771614443005494173904883, 526279357391401520621615883974791204], 'label': '46656.ja.288.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.g1.a1', 'old_label': '288.u1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
    • id: 216733452
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1'], 'contains': ['576.k1.a1', '864.be1.a1', '864.bi1.a1', '864.bo1.a1', '864.bp1.a1', '864.br1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [817, -1, 825, -1, 999, -1, 1322, -1], 'generators': [303381467301831984632523399028447236213, 95734917957429359405126502845972292587068, 10628652119101755771614443005494173904883, 64124670718523879045998849000898403973197, 526279357391401520621615883974791204], 'label': '46656.ja.288.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.v1.a1', 'old_label': '288.v1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 216733453
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.d1.a1', '36.g1.a1', '36.h1.a1', '162.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7240, -1, 8441, -1, 7145, -1, 8583, -1], 'generators': [106363043823389105545893585833978124276212, 806609900825601826955984788, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 4889323539096746538547753599744880709, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '46656.ja', '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': '5184.bv'}
    • id: 216733454
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '96.l1.a1', '144.h1.a1'], 'contains': ['576.d1.a1', '864.bf1.a1', '864.bh1.a1', '864.bi1.a1', '864.bt1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2836, -1, 4087, -1, 2299, -1, 2375, -1], 'generators': [303381467301831984632523399028447236213, 806609900825601826955984788, 180226866056773347083021461721293621697855, 10628380783110079692622515092497064064000, 526279357810177213463540390961872784], 'label': '46656.ja.288.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.b1.a1', 'old_label': '288.w1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1.a1', 'subgroup_fusion': None, 'weyl_group': '972.802'}
    • id: 216733455
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1', '96.l1.a1'], 'contains': ['576.g1.a1', '864.bf1.a1', '864.bj1.a1', '864.bu1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3229, -1, 3015, -1, 2125, -1, 2193, -1], 'generators': [303381467301831984632523399028447236213, 806609900825601826955984788, 10628380783110079692622515092497064064000, 170188679553435130165751915599078662555355, 526279357810177213463540390961872784], 'label': '46656.ja.288.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.j1.a1', 'old_label': '288.x1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1.a1', 'subgroup_fusion': None, 'weyl_group': '486.131'}
    • id: 216733456
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '96.k1.a1', '144.a1.a1'], 'contains': ['576.h1.a1', '864.bl1.a1', '864.bs1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [6502, -1, 4624, -1, 5338, -1, 3555, -1], 'generators': [806582924808469848094809744, 526279357391426248638338447114880243, 10628380783110079692622515092497064064000, 303907711292981967140573317956716054997, 106363298713707651554369414312181236029707], 'label': '46656.ja.288.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.a1.a1', 'old_label': '288.y1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.y1.a1', 'subgroup_fusion': None, 'weyl_group': '162.11'}
    • id: 216733457
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '96.k1.a1'], 'contains': ['576.i1.a1', '864.bm1.a1', '864.bs1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5836, -1, 4447, -1, 4843, -1, 2817, -1], 'generators': [806582924808469848094809744, 526279357391426248638338447114880243, 10628380783110079692622515092497064064000, 303907711292981967140573317956716054997, 116401213898738522940563810370348489169324], 'label': '46656.ja.288.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.k1.a1', 'old_label': '288.z1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.z1.a1', 'subgroup_fusion': None, 'weyl_group': '162.11'}
    • id: 216733458
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '96.l1.a1', '144.i1.a1'], 'contains': ['576.n1.a1', '864.bh1.a1', '864.bj1.a1', '864.bk1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4614, -1, 5480, -1, 4212, -1, 3163, -1], 'generators': [303381467301831984632523399028447236213, 806582924808469848094809744, 10628380783109691860669709973502134890388, 526279357810204189480672114507821508, 159560298770325050549561693285672192436955], 'label': '46656.ja.288.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.i1.a1', 'old_label': '288.ba1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
    • id: 216733459
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1.a1', '96.l1.a1'], 'contains': ['576.o1.a1', '864.bi1.a1', '864.bj1.a1', '864.bk1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4343, -1, 4963, -1, 4117, -1, 2743, -1], 'generators': [303381467301831984632523399028447236213, 806582924808469848094809744, 10628380783109691860669709973502134890388, 526279357810204189480672114507821508, 170188679553435130165751915599078662555355], 'label': '46656.ja.288.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.bb1.a1', 'old_label': '288.bb1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '162.19'}
    • id: 216733460
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1.a1', '96.l1.a1', '144.d1.a1', '144.e1.a1', '144.l1.a1'], 'contains': ['576.a1.a1', '864.bf1.a1', '864.bg1.a1', '864.bk1.a1', '864.bs1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4989, -1, 5108, -1, 5535, -1, 5527, -1], 'generators': [303381467301831984632523399028447236213, 806609900825601826955984788, 526279357810204189480672114507821508, 10628380783110079692622515092497064064000, 51704033854554571437363], 'label': '46656.ja.288.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '288.bc1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3494'}
    • id: 216733461
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '144.b1.a1'], 'contains': ['576.p1.a1', '864.bl1.a1', '864.bn1.a1', '864.bp1.a1', '864.bt1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [378, -1, 1931, -1, 1462, -1, 1812, -1], 'generators': [806582924808469848094809744, 74162585895017876807793029685849145093197, 10628380783110079692622515092497064064000, 106362772461180822312885285175687447357464, 303907711292175384215764848108664791093], 'label': '46656.ja.288.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.b1.a1', 'old_label': '288.bd1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '972.802'}
    • id: 216733462
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1'], 'contains': ['576.q1.a1', '864.bm1.a1', '864.bo1.a1', '864.bq1.a1', '864.br1.a1', '864.bt1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [429, -1, 1536, -1, 739, -1, 1238, -1], 'generators': [806582924808469848094809744, 95734663040283622995221501082320132455947, 74162585895017876807793029685849145093197, 10628380783110079692622515092497064064000, 303907711292175384215764848108664791093], 'label': '46656.ja.288.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.i1.a1', 'old_label': '288.be1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.be1.a1', 'subgroup_fusion': None, 'weyl_group': '486.236'}
    • id: 216733463
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1'], 'contains': ['576.r1.a1', '864.bl1.a1', '864.bu1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1553, -1, 308, -1, 664, -1, 1884, -1], 'generators': [806582924808469848094809744, 10628380783110079692622515092497064064000, 106362772461180822312885285175687447357464, 74162314549879162585470587006814584545773, 303907711292175384215764848108664791093], 'label': '46656.ja.288.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.j1.a1', 'old_label': '288.bf1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '486.131'}
    • id: 216733464
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['36.g1.a1', '36.h1.a1', '1458.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7519, -1, 8358, -1, 6971, -1, 8682, -1], 'generators': [106363043823389105545893585833978124276212, 806609900825601826955984788, 526279357810204189480672114507821508, 4889323539096746538547753599744880709, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 295241039866686163195720164433782901949, 212433027974419622066669321361961578524012, 51704033854554571437363], 'label': '46656.ja.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '46656.ja', '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': '5184.bv'}
    • id: 216733465
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1'], 'contains': ['576.s1.a1', '864.bm1.a1', '864.bu1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1287, -1, 126, -1, 289, -1, 1569, -1], 'generators': [806582924808469848094809744, 10628380783110079692622515092497064064000, 74162314549879162585470587006814584545773, 303907711292175384215764848108664791093, 116401213898738522940563810370348489169324], 'label': '46656.ja.288.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.j1.a1', 'old_label': '288.bg1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '486.131'}
    • id: 216733466
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1'], 'contains': ['576.s1.a2', '864.bm1.a1', '864.bu1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1287, -1, 233, -1, 289, -1, 1481, -1], 'generators': [806582924808469848094809744, 95734663040283622995221501082320132455947, 10628380783110079692622515092497064064000, 74162314549879162585470587006814584545773, 303907711292175384215764848108664791093], 'label': '46656.ja.288.bg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.j1.a1', 'old_label': '288.bg1.a2', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1.a2', 'subgroup_fusion': None, 'weyl_group': '486.131'}
    • id: 216733467
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '162.a1.a1'], 'contains': ['648.b1.a1', '648.q1.a1', '648.s1.a1', '2916.a1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [7413, -1, 9576, -1, 7458, -1, 8709, -1], 'generators': [5160668068034279637563046395935555445, 10628380783109273109697707710634166809840, 526279357391426248638338447114880243, 8683143932971954400776961842796037695, 191474750584276035266226527755940698012947, 20961536954955839867009601152064182920586], 'label': '46656.ja.324.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '46656.ja', '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': '144.186'}
    • id: 216733468
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '162.a1.a1'], 'contains': ['648.b1.a1', '648.c1.a1', '648.r1.a1', '648.v1.a1', '648.y1.a1', '972.a1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [6873, -1, 9622, -1, 7058, -1, 9540, -1], 'generators': [271362823044819707537240744665728244, 116400958982198772737288664322276851179491, 295241039866686187923735840869882632586, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 302837991359806377758241523003341283443], 'label': '46656.ja.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '46656.ja', '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': '144.186'}
    • id: 216733469
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['648.d1.a1', '648.e1.a1', '648.o1.a1', '972.b1.a1', '972.d1.a1', '1296.j1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [9718, -1, 5646, -1, 9732, -1, 5068, -1], 'generators': [8683143932971954400776961842796037695, 303092881674949634430682356042965385744, 10333682451203958183553111428496884386189, 295241039874623882848923312856951927800, 20671185247164736267520434613775381417842, 10628907036246266822906903469089534016147], 'label': '46656.ja.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1.a1', 'old_label': '324.c1.a1', 'projective_image': '46656.ja', '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': '72.44'}
    • id: 216733470
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['648.k1.a1', '648.p1.a1', '648.x1.a1', '972.a1.a1', '972.c1.a1', '1296.k1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [5318, -1, 6871, -1, 5089, -1, 5923, -1], 'generators': [95734391704287768655628053164098586071492, 8683143932971954400776961842796037695, 295767292394709794826891996777519880589, 10628380783110079692622515092497064064000, 302566629148151415373816942538671113604, 159855539810191736685781151981774231936514], 'label': '46656.ja.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1.a1', 'old_label': '324.d1.a1', 'projective_image': '46656.ja', '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': '144.183'}
    • id: 216733471
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '162.a1.a1'], 'contains': ['648.j1.a1', '648.q1.a1', '648.r1.a1', '2916.a1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [7482, -1, 9710, -1, 7519, -1, 8651, -1], 'generators': [10333156198067383221315917933164909118905, 526279358197957461991556476205226240, 8683143932971954400776961842796037695, 4889323539096746538547753599744880709, 418829652053207300505680884, 212141046534731461359761857275260497795347], 'label': '46656.ja.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.e1.a1', 'projective_image': '46656.ja', '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': '144.186'}
    • id: 216733472
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '162.a1.a1'], 'contains': ['648.j1.a1', '648.l1.a1', '648.s1.a1', '648.v1.a1', '648.z1.a1', '2916.b1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [6784, -1, 9310, -1, 6804, -1, 9032, -1], 'generators': [526279357391426248638338447114880243, 106363043823389912180515006384319285207639, 295241039867492770848301020249397883546, 8683143932971954400776961842796037695, 303092881675368488808440317543072183203, 51704033854554571437363], 'label': '46656.ja.324.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.f1.a1', 'projective_image': '46656.ja', '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': '144.186'}
    • id: 216733473
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '162.a1.a1'], 'contains': ['648.a1.a1', '648.b1.a1', '648.f1.a1', '648.h1.a1', '648.h1.a2', '648.i1.a1', '648.j1.a1', '648.m1.a1', '648.u1.a1', '972.d1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [8430, -1, 8173, -1, 8826, -1, 7158, -1], 'generators': [271362823044819707537240744665728244, 4889323539515524479147132005358403442, 295241039867492770848301020249397883546, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 302837991359806377758241523003341283443], 'label': '46656.ja.324.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.g1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 216733474
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '162.a1.a1'], 'contains': ['648.r1.a1', '648.s1.a1', '648.u1.a1', '2916.e1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [7601, -1, 9821, -1, 7722, -1, 8804, -1], 'generators': [271362823044819707537240744665728244, 106368187872404331818661945780748238896051, 4889323539096746538547753599744880709, 295241039867492746120284297941449525709, 10628380783110079692622515092497064064000, 302837991359806377758241523003341283443], 'label': '46656.ja.324.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.h1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 216733475
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.e1.a1', '72.a1.a1', '72.b1.a1', '96.a1.a1', '648.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8661, -1, 5508, -1, 9109, -1, 5146, -1], 'generators': [7968769049307653935737638642, 303381467301831984632523399028447236213, 806609900825601826955984788, 526279357810204189480672114507821508, 4889323539096746538547753599744880709, 10628380783110079692622515092497064064000, 7342044105036193097771690674969605241, 51704033854554571437363], 'label': '46656.ja.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.bt'}
    • id: 216733476
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '162.a1.a1'], 'contains': ['648.q1.a1', '648.t1.a1', '648.t1.a2', '648.u1.a1', '648.v1.a1', '2916.f1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [7277, -1, 9409, -1, 7348, -1, 8548, -1], 'generators': [271362823044819707537240744665728244, 116400958982198772737288664322276851179491, 295241039867073943451669619629046441005, 4889323539096746538547753599744880709, 10628380783110079692622515092497064064000, 302837991359806377758241523003341283443], 'label': '46656.ja.324.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.i1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 216733477
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1'], 'contains': ['864.b1.a1', '864.r1.a1', '864.bl1.a1', '1296.a1.a1', '1296.d1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3768, -1, 3403, -1, 3217, -1, 3416, -1], 'generators': [295495930182248325954817906088667208441, 806582924808469848094809744, 106067802792673666786562796867287085855601, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000], 'label': '46656.ja.432.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 216733478
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.d1.a1', '216.c1.a1'], 'contains': ['864.a1.a1', '864.y1.a1', '864.bs1.a1', '1296.b1.a1', '1296.c1.a1', '1296.d1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6954, -1, 5045, -1, 6458, -1, 5702, -1], 'generators': [806582924808469848094809744, 526279357391426248638338447114880243, 295241039867492770848301020249397883546, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000], 'label': '46656.ja.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '432.b1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '648.705'}
    • id: 216733479
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '216.a1.a1', '216.c1.a1', '216.h1.a1'], 'contains': ['864.a1.a1', '864.bc1.a1', '864.bg1.a1', '1296.e1.a1', '1296.f1.a1', '1296.f1.a2', '1296.g1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8695, -1, 6326, -1, 8468, -1, 6314, -1], 'generators': [806582924808469848094809744, 526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 302566629147732612700336125538638307444], 'label': '46656.ja.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '432.c1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 216733480
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.g1.a1'], 'contains': ['864.j1.a1', '864.m1.a1', '864.bn1.a1', '1296.a1.a1', '1296.i1.a1', '1296.l1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [628, -1, 2467, -1, 2638, -1, 3079, -1], 'generators': [295495930182248325954817906088667208441, 106067802792673666786562796867287085855601, 84790695297620968865831728937680811660014, 8683143932971954400776961842796037695, 10628380783109691912373743786211119168144], 'label': '46656.ja.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.d1.a1', 'old_label': '432.d1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 216733481
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.g1.a1'], 'contains': ['864.f1.a1', '864.o1.a1', '864.be1.a1', '1296.a1.a1', '1296.j1.a1', '1296.o1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2574, -1, 2974, -1, 3119, -1, 3266, -1], 'generators': [106067802792673666786562796867287085855601, 10628652119101755771614443005494173904883, 8683143932971954400776961842796037695, 526279357391401520621615883974791204, 20961536954955839840033584020085321871549], 'label': '46656.ja.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.e1.a1', 'old_label': '432.e1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 216733482
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.h1.a1'], 'contains': ['864.i1.a1', '864.s1.a1', '864.bt1.a1', '1296.d1.a1', '1296.k1.a1', '1296.l1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1390, -1, 3305, -1, 2935, -1, 4187, -1], 'generators': [526279358198009166025410762891264003, 295241039866686187923735840869882632586, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 159855539810191736685781151981774231936514], 'label': '46656.ja.432.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.b1.a1', 'old_label': '432.f1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 216733483
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.d1.a1', '144.h1.a1'], 'contains': ['864.d1.a1', '864.x1.a1', '864.bf1.a1', '1296.d1.a1', '1296.m1.a1', '1296.o1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4075, -1, 4233, -1, 3599, -1, 4269, -1], 'generators': [806582924808469848094809744, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 295241039866686163195720164433782901949], 'label': '46656.ja.432.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.c1.a1', 'old_label': '432.g1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 216733484
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '216.c1.a1', '216.d1.a1'], 'contains': ['864.e1.a1', '864.y1.a1', '864.bg1.a1', '1296.c1.a1', '1296.m1.a1', '1296.n1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [7829, -1, 7171, -1, 7923, -1, 6084, -1], 'generators': [526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783109273084969692034465828973603, 295241039866686163195720164433782901949, 51704033854554571437363], 'label': '46656.ja.432.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '432.h1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 216733485
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.i1.a1', '216.e1.a1'], 'contains': ['864.h1.a1', '864.z1.a1', '864.bk1.a1', '1296.b1.a1', '1296.m1.a1', '1296.n1.a1', '1296.o1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [5119, -1, 5760, -1, 5627, -1, 5614, -1], 'generators': [806582924808469848094809744, 10628380783109691860669709973502134890388, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 295241039866686163195720164433782901949], 'label': '46656.ja.432.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.e1.a1', 'old_label': '432.i1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 216733486
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.e1.a1', '72.e1.a1', '72.f1.a1', '72.g1.a1', '96.k1.a1', '648.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8352, -1, 5284, -1, 9021, -1, 4972, -1], 'generators': [7968769049307653935737638642, 806609900825601826955984788, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 4889323539096746538547753599744880709, 10628380783110079692622515092497064064000, 7342044105036193097771690674969605241, 51704033854554571437363], 'label': '46656.ja.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '46656.ja', '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': '1296.3494'}
    • id: 216733487
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '216.b1.a1', '216.d1.a1', '216.h1.a1'], 'contains': ['864.e1.a1', '864.ba1.a1', '864.bg1.a1', '1296.f1.a1', '1296.p1.a1', '1296.r1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8768, -1, 6718, -1, 8708, -1, 6777, -1], 'generators': [526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783109273084969692034465828973603, 303092881675368488808440317543072183203, 51704033854554571437363], 'label': '46656.ja.432.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '432.j1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 216733488
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '216.b1.a1', '216.d1.a1', '216.h1.a1'], 'contains': ['864.e1.a1', '864.ba1.a1', '864.bg1.a1', '1296.f1.a2', '1296.p1.a1', '1296.r1.a2'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8768, -1, 6537, -1, 8708, -1, 6855, -1], 'generators': [806609900825601826955984788, 526279357810204189480672114507821508, 8683143932971954400776961842796037695, 303092881675368488808440317543072183203, 51704033854554571437363], 'label': '46656.ja.432.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '432.j1.a2', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1.a2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 216733489
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '216.e1.a1'], 'contains': ['864.h1.a1', '864.bb1.a1', '864.bk1.a1', '1296.e1.a1', '1296.p1.a1', '1296.q1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [7161, -1, 8344, -1, 7609, -1, 6623, -1], 'generators': [526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203, 51704033854554571437363], 'label': '46656.ja.432.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.e1.a1', 'old_label': '432.k1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 216733490
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '216.b1.a1', '216.c1.a1', '216.i1.a1'], 'contains': ['864.e1.a1', '864.bc1.a1', '864.bs1.a1', '1296.g1.a1', '1296.q1.a1', '1296.r1.a1', '1296.r1.a2'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8551, -1, 6617, -1, 8555, -1, 7174, -1], 'generators': [526279358197957461991556476205226240, 8683143932971954400776961842796037695, 418829652053207300505680884, 10628380783110079692622515092497064064000, 303092881675368488808440317543072183203], 'label': '46656.ja.432.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '432.l1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 216733491
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.a1', '216.c1.a1', '216.h1.a1'], 'contains': ['864.a1.a1', '864.e1.a1', '864.ba1.a1', '1296.h1.a1', '1296.s1.a1', '1296.t1.a1', '1296.t1.a2'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [7976, -1, 7738, -1, 8192, -1, 7745, -1], 'generators': [806582924808469848094809744, 526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 7342044105036193097771690674969605241], 'label': '46656.ja.432.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '432.m1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 216733492
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.a1', '216.d1.a1', '216.h1.a1', '216.i1.a1'], 'contains': ['864.e1.a1', '864.bc1.a1', '1296.t1.a1', '1296.t1.a2', '1296.u1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8623, -1, 7071, -1, 8789, -1, 7836, -1], 'generators': [526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783109273084969692034465828973603, 10635722818067240058362515060758869099641, 51704033854554571437363], 'label': '46656.ja.432.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '432.n1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 216733493
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.a1', '216.e1.a1', '216.f1.a1', '216.g1.a1'], 'contains': ['864.h1.a1', '864.bd1.a1', '1296.s1.a1', '1296.u1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6063, -1, 8828, -1, 6737, -1, 8323, -1], 'generators': [526279357391426248638338447114880243, 8683143932971954400776961842796037695, 10628380783110079692622515092497064064000, 7596960639770528185922250573334958762, 51704033854554571437363], 'label': '46656.ja.432.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '432.o1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.o1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 216733494
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.a1', '144.h1.a1', '144.i1.a1'], 'contains': ['864.l1.a1', '864.p1.a1', '864.bh1.a1', '1296.l1.a1', '1296.o1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3261, -1, 4163, -1, 2805, -1, 3332, -1], 'generators': [180521564380141788362288626246736243603250, 295241039866686187923735840869882632586, 10628380783109691860669709973502134890388, 8683143932971954400776961842796037695, 526279357391401520621615883974791204], 'label': '46656.ja.432.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.g1.a1', 'old_label': '432.p1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.p1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
    • id: 216733495
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '216.j1.a1'], 'contains': ['864.u1.a1', '1296.ba1.a1', '3888.n1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [3553, -1, 3113, -1, 3413, -1, 4472, -1], 'generators': [202099328290927217204517559171341154336801, 10628907036247073405824291587544812057843, 351323245159463972521961075657549008027466, 20961536954955839840033584020085321871549, 526279357810177213463540390961872784], 'label': '46656.ja.432.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.j1.a1', 'old_label': '432.q1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.q1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 216733496
      {'ambient': '46656.ja', 'aut_centralizer_order': None, 'aut_label': '432.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.a1', '216.c1.a1', '216.d1.a1', '216.o1.a1'], 'contains': ['864.y1.a1', '864.ba1.a1', '864.bc1.a1', '1296.v1.a1', '1296.x1.a1', '1296.x1.a2', '1296.y1.a1'], 'core': '46656.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8169, -1, 7838, -1, 8009, -1, 8059, -1], 'generators': [526279357391426248638338447114880243, 10628380783109273084969692034465828973603, 303092881675368488808440317543072183203, 10333156198067383248291935023310637301949, 51704033854554571437363], 'label': '46656.ja.432.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '432.r1.a1', 'projective_image': '46656.ja', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.r1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}