Abstract group data - 1458.318

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '54.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 18, 'aut_gen_orders': [6, 18, 3], 'aut_gens': [[1, 3, 9, 27, 81], [983, 354, 981, 1026, 99], [47, 168, 981, 513, 1377], [1027, 561, 9, 513, 81]], 'aut_group': None, 'aut_hash': 299257164955112923, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 78732, 'aut_permdeg': 218, 'aut_perms': [115147370156216995826326435415996057266328256977976848902365495998906715074384900212002635785169319259820120009254218407780189274369065045278137168259319169959209027909144230437602895230049277362035688391822936977148753441895726950662148800782855180893710892438415964709830819599013006185985214677153377082015243486645803541193430683465594235553784835644872819375447177778649906030475358370225035338043373990975106420, 233278393117763606851452825131868225907318789711063060220751969685734684890544227838053988703433271363721355069513462096572298235746265453413572244279605108289496081630463365922035399424069399845092276687354234039859403170933003982172539740381455682463755037307343282076894061196183035445447484073158140929962425204807245882891552709408519272212979329640163178457193672135258508201355672515723983871713408402292514972, 250193094164378229951209590027078188786822980982611230708056854809390785965627341793122006242211330900194873560654767825376545011831162347572978058053141495979434408505525471696237568749208808906578338304158242344365307282949221240429008358096402519191751508158843995610410295267161808357881666849033556564026578545350088585171903906314831661211380802045817443333035834156591396068576680920259546154096503468975346943], 'aut_phi_ratio': 162.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 3, 1, 2], [3, 3, 2, 3], [3, 9, 6, 1], [6, 1, 2, 1], [6, 3, 1, 2], [6, 3, 2, 3], [6, 9, 6, 1], [9, 3, 6, 1], [9, 9, 4, 1], [9, 9, 12, 1], [9, 27, 6, 1], [9, 27, 12, 1], [18, 3, 6, 1], [18, 9, 4, 1], [18, 9, 12, 1], [18, 27, 6, 1], [18, 27, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3^3.C_3^4.C_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 3, 'autcent_group': '27.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 27, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': None, 'autcentquo_hash': 6045963717475089303, 'autcentquo_nilpotent': False, 'autcentquo_order': 2916, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3:S_3\\times C_3^3:S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 3, 8], [3, 9, 6], [6, 1, 2], [6, 3, 8], [6, 9, 6], [9, 3, 6], [9, 9, 16], [9, 27, 18], [18, 3, 6], [18, 9, 16], [18, 27, 18]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '243.37', 'commutator_count': 1, 'commutator_label': '27.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 318, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['729.318', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 3, 2, 4], [3, 9, 2, 3], [6, 1, 2, 1], [6, 3, 2, 4], [6, 9, 2, 3], [9, 3, 6, 1], [9, 9, 2, 8], [9, 27, 2, 9], [18, 3, 6, 1], [18, 9, 2, 8], [18, 27, 2, 9]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 19656, 'exponent': 18, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[9, 0, 6]], 'familial': False, 'frattini_label': '27.5', 'frattini_quotient': '54.15', 'hash': 318, 'hyperelementary': 3, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 3, 'inner_gen_orders': [3, 3, 3, 3, 3], 'inner_gens': [[1, 543, 9, 513, 81], [1000, 3, 495, 27, 90], [1, 975, 9, 27, 81], [973, 3, 9, 27, 81], [1, 21, 9, 27, 81]], 'inner_hash': 37, 'inner_nilpotent': True, 'inner_order': 243, 'inner_split': False, 'inner_tex': 'C_3^4:C_3', 'inner_used': [1, 2, 3, 5], 'irrC_degree': 9, 'irrQ_degree': 54, 'irrQ_dim': 54, 'irrR_degree': 18, 'irrep_stats': [[1, 54], [3, 48], [9, 12]], 'label': '1458.318', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C3^3.C3^3', 'ngens': 7, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [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': 26, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 114, 'number_divisions': 54, 'number_normal_subgroups': 92, 'number_subgroup_autclasses': 118, 'number_subgroup_classes': 402, 'number_subgroups': 1214, 'old_label': None, 'order': 1458, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 1], [3, 80], [6, 80], [9, 648], [18, 648]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 3, 6, 3], 'outer_gen_pows': [0, 18, 0, 0], 'outer_gens': [[2, 3, 9, 54, 1053], [1, 651, 9, 27, 567], [19, 6, 9, 540, 1395], [1, 3, 981, 27, 585]], 'outer_group': '324.165', 'outer_hash': 165, 'outer_nilpotent': False, 'outer_order': 324, 'outer_permdeg': 12, 'outer_perms': [134306469, 325, 207290595, 95074560], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2\\times S_3^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 83, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 26], [6, 24], [54, 2]], 'representations': {'PC': {'code': 25995321159807565550711461816875387, 'gens': [1, 2, 3, 4, 5], 'pres': [7, 3, 3, 3, 3, 2, 3, 3, 7603, 4544, 3474, 14367, 1061, 102, 2532, 166]}, 'Perm': {'d': 83, 'gens': [4056818722708954112583315078596886447209153947267041424404687952125046484787979958648958217892031599782920192000000000000, 147069248307040226282864316909429464915210689423392473989539837433471824864998844227916262972580460914976558785733, 1377024061744791030451904532286638822540539053233617334663373317412261663186571010434825778386956131856161488185954448884, 434852397243121841903738508636872870870223329922784147575092852482402881845895509490204652199293886827553470062155227587, 8549827396823706354984506769470825596107916065371793761249436756679107, 143139204459373239950628350093698015832105109958888976023325072521727612370983734222679461333931456093904926947119248884, 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000]}}, 'schur_multiplier': [3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 6], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_3^3.C_3^3', 'transitive_degree': 162, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 119223869
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 318, 'group_order': 1458, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 119223895
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 318, 'group_order': 1458, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 729, 'size': 1}
  • id: 119223906
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 318, 'group_order': 1458, 'label': '3A1', 'order': 3, 'powers': [4, 1], 'representative': 486, 'size': 1}
  • id: 119223917
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 318, 'group_order': 1458, 'label': '3A-1', 'order': 3, 'powers': [3, 1], 'representative': 972, 'size': 1}
  • id: 119223928
    {'aut_label': '3B1', 'centralizer': '3.c1', 'counter': 5, 'group_counter': 318, 'group_order': 1458, 'label': '3B1', 'order': 3, 'powers': [6, 1], 'representative': 540, 'size': 3}
  • id: 119223939
    {'aut_label': '3B1', 'centralizer': '3.c1', 'counter': 6, 'group_counter': 318, 'group_order': 1458, 'label': '3B-1', 'order': 3, 'powers': [5, 1], 'representative': 999, 'size': 3}
  • id: 119223950
    {'aut_label': '3C1', 'centralizer': '3.a1', 'counter': 7, 'group_counter': 318, 'group_order': 1458, 'label': '3C1', 'order': 3, 'powers': [8, 1], 'representative': 504, 'size': 3}
  • id: 119223961
    {'aut_label': '3C-1', 'centralizer': '3.a1', 'counter': 8, 'group_counter': 318, 'group_order': 1458, 'label': '3C-1', 'order': 3, 'powers': [7, 1], 'representative': 981, 'size': 3}
  • id: 119223972
    {'aut_label': '3D1', 'centralizer': '3.d1', 'counter': 9, 'group_counter': 318, 'group_order': 1458, 'label': '3D1', 'order': 3, 'powers': [10, 1], 'representative': 558, 'size': 3}
  • id: 119223870
    {'aut_label': '3D-1', 'centralizer': '3.d1', 'counter': 10, 'group_counter': 318, 'group_order': 1458, 'label': '3D-1', 'order': 3, 'powers': [9, 1], 'representative': 1008, 'size': 3}
  • id: 119223881
    {'aut_label': '3D1', 'centralizer': '3.d1', 'counter': 11, 'group_counter': 318, 'group_order': 1458, 'label': '3E1', 'order': 3, 'powers': [12, 1], 'representative': 531, 'size': 3}
  • id: 119223887
    {'aut_label': '3D-1', 'centralizer': '3.d1', 'counter': 12, 'group_counter': 318, 'group_order': 1458, 'label': '3E-1', 'order': 3, 'powers': [11, 1], 'representative': 1035, 'size': 3}
  • id: 119223888
    {'aut_label': '3F1', 'centralizer': '9.h1', 'counter': 13, 'group_counter': 318, 'group_order': 1458, 'label': '3F1', 'order': 3, 'powers': [14, 1], 'representative': 488, 'size': 9}
  • id: 119223889
    {'aut_label': '3F1', 'centralizer': '9.h1', 'counter': 14, 'group_counter': 318, 'group_order': 1458, 'label': '3F-1', 'order': 3, 'powers': [13, 1], 'representative': 973, 'size': 9}
  • id: 119223890
    {'aut_label': '3F1', 'centralizer': '9.h1', 'counter': 15, 'group_counter': 318, 'group_order': 1458, 'label': '3G1', 'order': 3, 'powers': [16, 1], 'representative': 506, 'size': 9}
  • id: 119223891
    {'aut_label': '3F1', 'centralizer': '9.h1', 'counter': 16, 'group_counter': 318, 'group_order': 1458, 'label': '3G-1', 'order': 3, 'powers': [15, 1], 'representative': 982, 'size': 9}
  • id: 119223892
    {'aut_label': '3F1', 'centralizer': '9.h1', 'counter': 17, 'group_counter': 318, 'group_order': 1458, 'label': '3H1', 'order': 3, 'powers': [18, 1], 'representative': 497, 'size': 9}
  • id: 119223893
    {'aut_label': '3F1', 'centralizer': '9.h1', 'counter': 18, 'group_counter': 318, 'group_order': 1458, 'label': '3H-1', 'order': 3, 'powers': [17, 1], 'representative': 991, 'size': 9}
  • id: 119223894
    {'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 19, 'group_counter': 318, 'group_order': 1458, 'label': '6A1', 'order': 6, 'powers': [3, 2], 'representative': 243, 'size': 1}
  • id: 119223896
    {'aut_label': '6A1', 'centralizer': '1.a1', 'counter': 20, 'group_counter': 318, 'group_order': 1458, 'label': '6A-1', 'order': 6, 'powers': [4, 2], 'representative': 1215, 'size': 1}
  • id: 119223897
    {'aut_label': '6B1', 'centralizer': '3.c1', 'counter': 21, 'group_counter': 318, 'group_order': 1458, 'label': '6B1', 'order': 6, 'powers': [5, 2], 'representative': 270, 'size': 3}
  • id: 119223898
    {'aut_label': '6B1', 'centralizer': '3.c1', 'counter': 22, 'group_counter': 318, 'group_order': 1458, 'label': '6B-1', 'order': 6, 'powers': [6, 2], 'representative': 297, 'size': 3}
  • id: 119223899
    {'aut_label': '6C1', 'centralizer': '3.a1', 'counter': 23, 'group_counter': 318, 'group_order': 1458, 'label': '6C1', 'order': 6, 'powers': [7, 2], 'representative': 252, 'size': 3}
  • id: 119223900
    {'aut_label': '6C-1', 'centralizer': '3.a1', 'counter': 24, 'group_counter': 318, 'group_order': 1458, 'label': '6C-1', 'order': 6, 'powers': [8, 2], 'representative': 261, 'size': 3}
  • id: 119223901
    {'aut_label': '6D1', 'centralizer': '3.d1', 'counter': 25, 'group_counter': 318, 'group_order': 1458, 'label': '6D1', 'order': 6, 'powers': [9, 2], 'representative': 279, 'size': 3}
  • id: 119223902
    {'aut_label': '6D-1', 'centralizer': '3.d1', 'counter': 26, 'group_counter': 318, 'group_order': 1458, 'label': '6D-1', 'order': 6, 'powers': [10, 2], 'representative': 315, 'size': 3}
  • id: 119223903
    {'aut_label': '6D1', 'centralizer': '3.d1', 'counter': 27, 'group_counter': 318, 'group_order': 1458, 'label': '6E1', 'order': 6, 'powers': [11, 2], 'representative': 306, 'size': 3}
  • id: 119223904
    {'aut_label': '6D-1', 'centralizer': '3.d1', 'counter': 28, 'group_counter': 318, 'group_order': 1458, 'label': '6E-1', 'order': 6, 'powers': [12, 2], 'representative': 288, 'size': 3}
  • id: 119223905
    {'aut_label': '6F1', 'centralizer': '9.h1', 'counter': 29, 'group_counter': 318, 'group_order': 1458, 'label': '6F1', 'order': 6, 'powers': [13, 2], 'representative': 244, 'size': 9}
  • id: 119223907
    {'aut_label': '6F1', 'centralizer': '9.h1', 'counter': 30, 'group_counter': 318, 'group_order': 1458, 'label': '6F-1', 'order': 6, 'powers': [14, 2], 'representative': 245, 'size': 9}
  • id: 119223908
    {'aut_label': '6F1', 'centralizer': '9.h1', 'counter': 31, 'group_counter': 318, 'group_order': 1458, 'label': '6G1', 'order': 6, 'powers': [15, 2], 'representative': 253, 'size': 9}
  • id: 119223909
    {'aut_label': '6F1', 'centralizer': '9.h1', 'counter': 32, 'group_counter': 318, 'group_order': 1458, 'label': '6G-1', 'order': 6, 'powers': [16, 2], 'representative': 263, 'size': 9}
  • id: 119223910
    {'aut_label': '6F1', 'centralizer': '9.h1', 'counter': 33, 'group_counter': 318, 'group_order': 1458, 'label': '6H1', 'order': 6, 'powers': [17, 2], 'representative': 262, 'size': 9}
  • id: 119223911
    {'aut_label': '6F1', 'centralizer': '9.h1', 'counter': 34, 'group_counter': 318, 'group_order': 1458, 'label': '6H-1', 'order': 6, 'powers': [18, 2], 'representative': 254, 'size': 9}
  • id: 119223912
    {'aut_label': '9A1', 'centralizer': '3.a1', 'counter': 35, 'group_counter': 318, 'group_order': 1458, 'label': '9A1', 'order': 9, 'powers': [37, 3], 'representative': 162, 'size': 3}
  • id: 119223913
    {'aut_label': '9A1', 'centralizer': '3.a1', 'counter': 36, 'group_counter': 318, 'group_order': 1458, 'label': '9A-1', 'order': 9, 'powers': [38, 4], 'representative': 1296, 'size': 3}
  • id: 119223914
    {'aut_label': '9A1', 'centralizer': '3.a1', 'counter': 37, 'group_counter': 318, 'group_order': 1458, 'label': '9A2', 'order': 9, 'powers': [39, 4], 'representative': 324, 'size': 3}
  • id: 119223915
    {'aut_label': '9A1', 'centralizer': '3.a1', 'counter': 38, 'group_counter': 318, 'group_order': 1458, 'label': '9A-2', 'order': 9, 'powers': [40, 3], 'representative': 1134, 'size': 3}
  • id: 119223916
    {'aut_label': '9A1', 'centralizer': '3.a1', 'counter': 39, 'group_counter': 318, 'group_order': 1458, 'label': '9A4', 'order': 9, 'powers': [36, 3], 'representative': 648, 'size': 3}
  • id: 119223918
    {'aut_label': '9A1', 'centralizer': '3.a1', 'counter': 40, 'group_counter': 318, 'group_order': 1458, 'label': '9A-4', 'order': 9, 'powers': [35, 4], 'representative': 810, 'size': 3}
  • id: 119223919
    {'aut_label': '9B1', 'centralizer': '9.b1', 'counter': 41, 'group_counter': 318, 'group_order': 1458, 'label': '9B1', 'order': 9, 'powers': [42, 3], 'representative': 216, 'size': 9}
  • id: 119223920
    {'aut_label': '9B1', 'centralizer': '9.b1', 'counter': 42, 'group_counter': 318, 'group_order': 1458, 'label': '9B-1', 'order': 9, 'powers': [41, 4], 'representative': 1323, 'size': 9}
  • id: 119223921
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 43, 'group_counter': 318, 'group_order': 1458, 'label': '9C1', 'order': 9, 'powers': [44, 3], 'representative': 164, 'size': 9}
  • id: 119223922
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 44, 'group_counter': 318, 'group_order': 1458, 'label': '9C-1', 'order': 9, 'powers': [43, 4], 'representative': 1297, 'size': 9}
  • id: 119223923
    {'aut_label': '9B1', 'centralizer': '9.b1', 'counter': 45, 'group_counter': 318, 'group_order': 1458, 'label': '9D1', 'order': 9, 'powers': [46, 3], 'representative': 189, 'size': 9}
  • id: 119223924
    {'aut_label': '9B1', 'centralizer': '9.b1', 'counter': 46, 'group_counter': 318, 'group_order': 1458, 'label': '9D-1', 'order': 9, 'powers': [45, 4], 'representative': 1350, 'size': 9}
  • id: 119223925
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 47, 'group_counter': 318, 'group_order': 1458, 'label': '9E1', 'order': 9, 'powers': [48, 3], 'representative': 163, 'size': 9}
  • id: 119223926
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 48, 'group_counter': 318, 'group_order': 1458, 'label': '9E-1', 'order': 9, 'powers': [47, 4], 'representative': 1298, 'size': 9}
  • id: 119223927
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 49, 'group_counter': 318, 'group_order': 1458, 'label': '9F1', 'order': 9, 'powers': [50, 3], 'representative': 704, 'size': 9}
  • id: 119223929
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 50, 'group_counter': 318, 'group_order': 1458, 'label': '9F-1', 'order': 9, 'powers': [49, 4], 'representative': 1324, 'size': 9}
  • id: 119223930
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 51, 'group_counter': 318, 'group_order': 1458, 'label': '9G1', 'order': 9, 'powers': [52, 3], 'representative': 182, 'size': 9}
  • id: 119223931
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 52, 'group_counter': 318, 'group_order': 1458, 'label': '9G-1', 'order': 9, 'powers': [51, 4], 'representative': 1306, 'size': 9}
  • id: 119223932
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 53, 'group_counter': 318, 'group_order': 1458, 'label': '9H1', 'order': 9, 'powers': [54, 3], 'representative': 1189, 'size': 9}
  • id: 119223933
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 54, 'group_counter': 318, 'group_order': 1458, 'label': '9H-1', 'order': 9, 'powers': [53, 4], 'representative': 1325, 'size': 9}
  • id: 119223934
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 55, 'group_counter': 318, 'group_order': 1458, 'label': '9I1', 'order': 9, 'powers': [56, 3], 'representative': 676, 'size': 9}
  • id: 119223935
    {'aut_label': '9C1', 'centralizer': '9.h1', 'counter': 56, 'group_counter': 318, 'group_order': 1458, 'label': '9I-1', 'order': 9, 'powers': [55, 4], 'representative': 1352, 'size': 9}
  • id: 119223936
    {'aut_label': '9J1', 'centralizer': '27.h1', 'counter': 57, 'group_counter': 318, 'group_order': 1458, 'label': '9J1', 'order': 9, 'powers': [58, 3], 'representative': 177, 'size': 27}
  • id: 119223937
    {'aut_label': '9J1', 'centralizer': '27.h1', 'counter': 58, 'group_counter': 318, 'group_order': 1458, 'label': '9J-1', 'order': 9, 'powers': [57, 4], 'representative': 1299, 'size': 27}
  • id: 119223938
    {'aut_label': '9J1', 'centralizer': '27.h1', 'counter': 59, 'group_counter': 318, 'group_order': 1458, 'label': '9K1', 'order': 9, 'powers': [60, 4], 'representative': 183, 'size': 27}
  • id: 119223940
    {'aut_label': '9J1', 'centralizer': '27.h1', 'counter': 60, 'group_counter': 318, 'group_order': 1458, 'label': '9K-1', 'order': 9, 'powers': [59, 3], 'representative': 330, 'size': 27}
  • id: 119223941
    {'aut_label': '9J1', 'centralizer': '27.h1', 'counter': 61, 'group_counter': 318, 'group_order': 1458, 'label': '9L1', 'order': 9, 'powers': [62, 3], 'representative': 492, 'size': 27}
  • id: 119223942
    {'aut_label': '9J1', 'centralizer': '27.h1', 'counter': 62, 'group_counter': 318, 'group_order': 1458, 'label': '9L-1', 'order': 9, 'powers': [61, 4], 'representative': 3, 'size': 27}
  • id: 119223943
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 63, 'group_counter': 318, 'group_order': 1458, 'label': '9M1', 'order': 9, 'powers': [64, 4], 'representative': 719, 'size': 27}
  • id: 119223944
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 64, 'group_counter': 318, 'group_order': 1458, 'label': '9M-1', 'order': 9, 'powers': [63, 3], 'representative': 328, 'size': 27}
  • id: 119223945
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 65, 'group_counter': 318, 'group_order': 1458, 'label': '9N1', 'order': 9, 'powers': [66, 3], 'representative': 1184, 'size': 27}
  • id: 119223946
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 66, 'group_counter': 318, 'group_order': 1458, 'label': '9N-1', 'order': 9, 'powers': [65, 4], 'representative': 1303, 'size': 27}
  • id: 119223947
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 67, 'group_counter': 318, 'group_order': 1458, 'label': '9O1', 'order': 9, 'powers': [68, 4], 'representative': 691, 'size': 27}
  • id: 119223948
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 68, 'group_counter': 318, 'group_order': 1458, 'label': '9O-1', 'order': 9, 'powers': [67, 3], 'representative': 329, 'size': 27}
  • id: 119223949
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 69, 'group_counter': 318, 'group_order': 1458, 'label': '9P1', 'order': 9, 'powers': [70, 3], 'representative': 1210, 'size': 27}
  • id: 119223951
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 70, 'group_counter': 318, 'group_order': 1458, 'label': '9P-1', 'order': 9, 'powers': [69, 4], 'representative': 1304, 'size': 27}
  • id: 119223952
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 71, 'group_counter': 318, 'group_order': 1458, 'label': '9Q1', 'order': 9, 'powers': [72, 4], 'representative': 1034, 'size': 27}
  • id: 119223953
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 72, 'group_counter': 318, 'group_order': 1458, 'label': '9Q-1', 'order': 9, 'powers': [71, 3], 'representative': 490, 'size': 27}
  • id: 119223954
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 73, 'group_counter': 318, 'group_order': 1458, 'label': '9R1', 'order': 9, 'powers': [74, 3], 'representative': 1004, 'size': 27}
  • id: 119223955
    {'aut_label': '9M1', 'centralizer': '27.r1', 'counter': 74, 'group_counter': 318, 'group_order': 1458, 'label': '9R-1', 'order': 9, 'powers': [73, 4], 'representative': 7, 'size': 27}
  • id: 119223956
    {'aut_label': '18A1', 'centralizer': '3.a1', 'counter': 75, 'group_counter': 318, 'group_order': 1458, 'label': '18A1', 'order': 18, 'powers': [35, 19], 'representative': 81, 'size': 3}
  • id: 119223957
    {'aut_label': '18A1', 'centralizer': '3.a1', 'counter': 76, 'group_counter': 318, 'group_order': 1458, 'label': '18A-1', 'order': 18, 'powers': [36, 20], 'representative': 1377, 'size': 3}
  • id: 119223958
    {'aut_label': '18A1', 'centralizer': '3.a1', 'counter': 77, 'group_counter': 318, 'group_order': 1458, 'label': '18A5', 'order': 18, 'powers': [40, 20], 'representative': 405, 'size': 3}
  • id: 119223959
    {'aut_label': '18A1', 'centralizer': '3.a1', 'counter': 78, 'group_counter': 318, 'group_order': 1458, 'label': '18A-5', 'order': 18, 'powers': [39, 19], 'representative': 1053, 'size': 3}
  • id: 119223960
    {'aut_label': '18A1', 'centralizer': '3.a1', 'counter': 79, 'group_counter': 318, 'group_order': 1458, 'label': '18A7', 'order': 18, 'powers': [38, 19], 'representative': 567, 'size': 3}
  • id: 119223962
    {'aut_label': '18A1', 'centralizer': '3.a1', 'counter': 80, 'group_counter': 318, 'group_order': 1458, 'label': '18A-7', 'order': 18, 'powers': [37, 20], 'representative': 891, 'size': 3}
  • id: 119223963
    {'aut_label': '18B1', 'centralizer': '9.b1', 'counter': 81, 'group_counter': 318, 'group_order': 1458, 'label': '18B1', 'order': 18, 'powers': [41, 19], 'representative': 108, 'size': 9}
  • id: 119223964
    {'aut_label': '18B1', 'centralizer': '9.b1', 'counter': 82, 'group_counter': 318, 'group_order': 1458, 'label': '18B-1', 'order': 18, 'powers': [42, 20], 'representative': 459, 'size': 9}
  • id: 119223965
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 83, 'group_counter': 318, 'group_order': 1458, 'label': '18C1', 'order': 18, 'powers': [43, 19], 'representative': 82, 'size': 9}
  • id: 119223966
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 84, 'group_counter': 318, 'group_order': 1458, 'label': '18C-1', 'order': 18, 'powers': [44, 20], 'representative': 407, 'size': 9}
  • id: 119223967
    {'aut_label': '18B1', 'centralizer': '9.b1', 'counter': 85, 'group_counter': 318, 'group_order': 1458, 'label': '18D1', 'order': 18, 'powers': [45, 19], 'representative': 135, 'size': 9}
  • id: 119223968
    {'aut_label': '18B1', 'centralizer': '9.b1', 'counter': 86, 'group_counter': 318, 'group_order': 1458, 'label': '18D-1', 'order': 18, 'powers': [46, 20], 'representative': 432, 'size': 9}
  • id: 119223969
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 87, 'group_counter': 318, 'group_order': 1458, 'label': '18E1', 'order': 18, 'powers': [47, 19], 'representative': 83, 'size': 9}
  • id: 119223970
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 88, 'group_counter': 318, 'group_order': 1458, 'label': '18E-1', 'order': 18, 'powers': [48, 20], 'representative': 406, 'size': 9}
  • id: 119223971
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 89, 'group_counter': 318, 'group_order': 1458, 'label': '18F1', 'order': 18, 'powers': [49, 19], 'representative': 109, 'size': 9}
  • id: 119223973
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 90, 'group_counter': 318, 'group_order': 1458, 'label': '18F-1', 'order': 18, 'powers': [50, 20], 'representative': 416, 'size': 9}
  • id: 119223974
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 91, 'group_counter': 318, 'group_order': 1458, 'label': '18G1', 'order': 18, 'powers': [51, 19], 'representative': 91, 'size': 9}
  • id: 119223975
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 92, 'group_counter': 318, 'group_order': 1458, 'label': '18G-1', 'order': 18, 'powers': [52, 20], 'representative': 434, 'size': 9}
  • id: 119223976
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 93, 'group_counter': 318, 'group_order': 1458, 'label': '18H1', 'order': 18, 'powers': [53, 19], 'representative': 110, 'size': 9}
  • id: 119223977
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 94, 'group_counter': 318, 'group_order': 1458, 'label': '18H-1', 'order': 18, 'powers': [54, 20], 'representative': 460, 'size': 9}
  • id: 119223978
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 95, 'group_counter': 318, 'group_order': 1458, 'label': '18I1', 'order': 18, 'powers': [55, 19], 'representative': 137, 'size': 9}
  • id: 119223979
    {'aut_label': '18C1', 'centralizer': '9.h1', 'counter': 96, 'group_counter': 318, 'group_order': 1458, 'label': '18I-1', 'order': 18, 'powers': [56, 20], 'representative': 433, 'size': 9}
  • id: 119223980
    {'aut_label': '18J1', 'centralizer': '27.h1', 'counter': 97, 'group_counter': 318, 'group_order': 1458, 'label': '18J1', 'order': 18, 'powers': [57, 19], 'representative': 84, 'size': 27}
  • id: 119223981
    {'aut_label': '18J1', 'centralizer': '27.h1', 'counter': 98, 'group_counter': 318, 'group_order': 1458, 'label': '18J-1', 'order': 18, 'powers': [58, 20], 'representative': 411, 'size': 27}
  • id: 119223982
    {'aut_label': '18J1', 'centralizer': '27.h1', 'counter': 99, 'group_counter': 318, 'group_order': 1458, 'label': '18K1', 'order': 18, 'powers': [59, 20], 'representative': 87, 'size': 27}
  • id: 119223871
    {'aut_label': '18J1', 'centralizer': '27.h1', 'counter': 100, 'group_counter': 318, 'group_order': 1458, 'label': '18K-1', 'order': 18, 'powers': [60, 19], 'representative': 408, 'size': 27}
  • id: 119223872
    {'aut_label': '18J1', 'centralizer': '27.h1', 'counter': 101, 'group_counter': 318, 'group_order': 1458, 'label': '18L1', 'order': 18, 'powers': [61, 19], 'representative': 246, 'size': 27}
  • id: 119223873
    {'aut_label': '18J1', 'centralizer': '27.h1', 'counter': 102, 'group_counter': 318, 'group_order': 1458, 'label': '18L-1', 'order': 18, 'powers': [62, 20], 'representative': 249, 'size': 27}
  • id: 119223874
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 103, 'group_counter': 318, 'group_order': 1458, 'label': '18M1', 'order': 18, 'powers': [63, 20], 'representative': 85, 'size': 27}
  • id: 119223875
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 104, 'group_counter': 318, 'group_order': 1458, 'label': '18M-1', 'order': 18, 'powers': [64, 19], 'representative': 413, 'size': 27}
  • id: 119223876
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 105, 'group_counter': 318, 'group_order': 1458, 'label': '18N1', 'order': 18, 'powers': [65, 19], 'representative': 88, 'size': 27}
  • id: 119223877
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 106, 'group_counter': 318, 'group_order': 1458, 'label': '18N-1', 'order': 18, 'powers': [66, 20], 'representative': 410, 'size': 27}
  • id: 119223878
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 107, 'group_counter': 318, 'group_order': 1458, 'label': '18O1', 'order': 18, 'powers': [67, 20], 'representative': 86, 'size': 27}
  • id: 119223879
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 108, 'group_counter': 318, 'group_order': 1458, 'label': '18O-1', 'order': 18, 'powers': [68, 19], 'representative': 412, 'size': 27}
  • id: 119223880
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 109, 'group_counter': 318, 'group_order': 1458, 'label': '18P1', 'order': 18, 'powers': [69, 19], 'representative': 89, 'size': 27}
  • id: 119223882
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 110, 'group_counter': 318, 'group_order': 1458, 'label': '18P-1', 'order': 18, 'powers': [70, 20], 'representative': 409, 'size': 27}
  • id: 119223883
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 111, 'group_counter': 318, 'group_order': 1458, 'label': '18Q1', 'order': 18, 'powers': [71, 20], 'representative': 247, 'size': 27}
  • id: 119223884
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 112, 'group_counter': 318, 'group_order': 1458, 'label': '18Q-1', 'order': 18, 'powers': [72, 19], 'representative': 251, 'size': 27}
  • id: 119223885
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 113, 'group_counter': 318, 'group_order': 1458, 'label': '18R1', 'order': 18, 'powers': [73, 19], 'representative': 250, 'size': 27}
  • id: 119223886
    {'aut_label': '18M1', 'centralizer': '27.r1', 'counter': 114, 'group_counter': 318, 'group_order': 1458, 'label': '18R-1', 'order': 18, 'powers': [74, 20], 'representative': 248, 'size': 27}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 6583641
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 6583652
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 6583663
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6583674
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1d', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 6583685
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1], 'schur_index': 1}
  • id: 6583691
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1f', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1], 'schur_index': 1}
  • id: 6583692
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1g', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1], 'schur_index': 1}
  • id: 6583693
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1h', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2], 'schur_index': 1}
  • id: 6583694
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, 2, -1, 2], 'schur_index': 1}
  • id: 6583642
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1j', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1], 'schur_index': 1}
  • id: 6583643
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1k', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6583644
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1l', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 6583645
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1m', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2], 'schur_index': 1}
  • id: 6583646
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1n', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1], 'schur_index': 1}
  • id: 6583647
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1o', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6583648
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6583649
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1q', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 6583650
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1r', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, -2, 1, -2, -2, 1, 1], 'schur_index': 1}
  • id: 6583651
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1s', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, 2, -1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, -2, 1, 1, 1, -2, 1, 1, 1, 1, -2, -2, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1], 'schur_index': 1}
  • id: 6583653
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1t', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, -2, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, -2, 1, -2, 1, 1, -2, -2, 1], 'schur_index': 1}
  • id: 6583654
    {'cdim': 1, 'counter': 21, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1u', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, -2, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, -2, 1, -2, -2, 1, -2, 1, 1, 1, 1, 1, -2], 'schur_index': 1}
  • id: 6583655
    {'cdim': 1, 'counter': 22, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1v', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, -2, 1, -2, 1, -2], 'schur_index': 1}
  • id: 6583656
    {'cdim': 1, 'counter': 23, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1w', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1], 'schur_index': 1}
  • id: 6583657
    {'cdim': 1, 'counter': 24, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1x', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, 1, -2, 1, -2, -2, -2, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6583658
    {'cdim': 1, 'counter': 25, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1y', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 6583659
    {'cdim': 1, 'counter': 26, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1z', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 1, -2, 1, 1, 1, -2, 1, 1, -2], 'schur_index': 1}
  • id: 6583660
    {'cdim': 1, 'counter': 27, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1aa', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -2, 1], 'schur_index': 1}
  • id: 6583661
    {'cdim': 1, 'counter': 28, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.1ab', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6583662
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3a', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, -3, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583664
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3b', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, 6, 0, 0, 0, 0, 6, -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, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 6, 0, 0, 0, 6, 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], 'schur_index': 1}
  • id: 6583665
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3c', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, -3, 0, 0, 0, 0, -3, -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, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, -3, 0, 0, 0, -3, 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], 'schur_index': 1}
  • id: 6583666
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3d', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 6, -3, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 6, 0, 6, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583667
    {'cdim': 3, 'counter': 33, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3e', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, -3, 6, -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, 6, -3, 0, 0, 0, 0, 0, -3, 0, -3, 0, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583668
    {'cdim': 3, 'counter': 34, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3f', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, -3, -3, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, -3, -3, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, -3, 0, -3, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583669
    {'cdim': 3, 'counter': 35, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3g', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, -3, -3, 6, 6, -3, -3, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, -3, 6, 6, -3, -3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583670
    {'cdim': 3, 'counter': 36, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3h', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, -3, 6, -3, -3, 6, -3, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, -3, -3, -3, 6, 6, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583671
    {'cdim': 3, 'counter': 37, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3i', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583672
    {'cdim': 3, 'counter': 38, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3j', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, -3, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 6, 0, 0, 0, 0, -3, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, 6, -3, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583673
    {'cdim': 3, 'counter': 39, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3k', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, -3, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, -3, 0, 0, 0, 0, -3, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, 0, -3, -3, 0, 0, 0, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583675
    {'cdim': 3, 'counter': 40, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3l', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 6, 6, -3, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 0, 0, 6, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, -3, 6, 0, 0, 0, -3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583676
    {'cdim': 3, 'counter': 41, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3m', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, -6, -6, 3, -6, 3, 3, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, -3, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583677
    {'cdim': 3, 'counter': 42, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3n', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, -6, -6, 3, -6, 3, 3, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, 6, 0, 0, 0, 0, 6, -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, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, -6, 0, 0, 0, -6, 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], 'schur_index': 1}
  • id: 6583678
    {'cdim': 3, 'counter': 43, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3o', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, -6, -6, 3, -6, 3, 3, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, -3, 0, 0, 0, 0, -3, -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, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, 3, 0, 0, 0, 3, 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], 'schur_index': 1}
  • id: 6583679
    {'cdim': 3, 'counter': 44, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3p', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, -6, -6, -6, 3, 3, 3, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 6, -3, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, -6, 0, -6, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583680
    {'cdim': 3, 'counter': 45, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3q', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, -6, -6, -6, 3, 3, 3, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, -3, 6, -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, -6, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 3, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583681
    {'cdim': 3, 'counter': 46, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3r', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, -6, -6, -6, 3, 3, 3, 3, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, -3, -3, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 3, 0, 3, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583682
    {'cdim': 3, 'counter': 47, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3s', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, -3, -3, 6, 6, -3, -3, -6, -6, 3, 3, -6, 3, 3, 3, 3, -6, 3, -6, -6, 3, 3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583683
    {'cdim': 3, 'counter': 48, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3t', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, -3, 6, -3, -3, 6, -3, -6, -6, 3, 3, -6, 3, 3, 3, 3, -6, 3, 3, 3, -6, -6, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583684
    {'cdim': 3, 'counter': 49, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3u', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, -3, 6, -3, -3, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, -6, -6, 3, 3, -6, 3, 3, 3, 3, -6, -6, 3, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583686
    {'cdim': 3, 'counter': 50, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3v', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -6, -6, 3, 3, 3, -6, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 6, 0, 0, 0, 0, -3, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, -6, 3, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583687
    {'cdim': 3, 'counter': 51, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3w', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -6, -6, 3, 3, 3, -6, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, -3, 0, 0, 0, 0, -3, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 0, 3, 3, 0, 0, 0, -6, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583688
    {'cdim': 3, 'counter': 52, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.3x', 'multiplicity': 2, 'nt': [18, 15], 'qdim': 6, 'qvalues': [6, -6, 6, 6, 6, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -6, -6, 3, 3, 3, -6, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 0, 0, 6, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, -6, 0, 0, 0, 3, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583689
    {'cdim': 9, 'counter': 53, 'faithful': False, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.9a', 'multiplicity': 6, 'nt': [81, 0], 'qdim': 54, 'qvalues': [54, 54, -27, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6583690
    {'cdim': 9, 'counter': 54, 'faithful': True, 'group': '1458.318', 'group_order': 1458, 'image': None, 'label': '1458.318.9b', 'multiplicity': 6, 'nt': [162, 0], 'qdim': 54, 'qvalues': [54, -54, -27, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 14267832
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1458, 'label': '1458.318.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 14267893
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 51, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 243, 'label': '1458.318.1aa1', 'nt': [6, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]]]}
  • id: 14267894
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 52, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 243, 'label': '1458.318.1aa2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]]]}
  • id: 14267895
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 53, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 243, 'label': '1458.318.1ab1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]]]}
  • id: 14267896
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 54, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 243, 'label': '1458.318.1ab2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]]]}
  • id: 14267858
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 729, 'label': '1458.318.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 14267869
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[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, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]]]}
  • id: 14267880
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[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, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 14267891
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1d1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[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, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]]]}
  • id: 14267902
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1d2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[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, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]]]}
  • id: 14267913
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[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, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]]]}
  • id: 14267924
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[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, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]]]}
  • id: 14267935
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1f1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 14267833
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  • id: 14267844
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1g1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]]]}
  • id: 14267850
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1g2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]]]}
  • id: 14267851
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1h1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]]]}
  • id: 14267852
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 486, 'label': '1458.318.1h2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]]]}
  • id: 14267853
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 486, 'label': '1458.318.1i1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[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, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]]]}
  • id: 14267854
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 486, 'label': '1458.318.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[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, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]]]}
  • id: 14267855
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.d1', 'kernel_order': 486, 'label': '1458.318.1j1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[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, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]]]}
  • id: 14267856
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.d1', 'kernel_order': 486, 'label': '1458.318.1j2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[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, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]]]}
  • id: 14267857
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  • id: 14267859
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.d1', 'kernel_order': 486, 'label': '1458.318.1k2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 14267860
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 486, 'label': '1458.318.1l1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 14267861
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 486, 'label': '1458.318.1l2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 14267862
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 486, 'label': '1458.318.1m1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]]]}
  • id: 14267863
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 486, 'label': '1458.318.1m2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]]]}
  • id: 14267864
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 25, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 486, 'label': '1458.318.1n1', 'nt': [3, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]]]}
  • id: 14267865
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 26, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 486, 'label': '1458.318.1n2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]]]}
  • id: 14267866
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 27, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 486, 'label': '1458.318.1o1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]]]}
  • id: 14267867
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  • id: 14267868
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 29, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 243, 'label': '1458.318.1p1', 'nt': [6, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[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, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]]]}
  • id: 14267870
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 30, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 243, 'label': '1458.318.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[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, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 14267871
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 31, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 243, 'label': '1458.318.1q1', 'nt': [6, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[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, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]]]}
  • id: 14267872
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 32, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 243, 'label': '1458.318.1q2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[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, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 14267873
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 33, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 243, 'label': '1458.318.1r1', 'nt': [6, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[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, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]]]}
  • id: 14267874
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 34, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 243, 'label': '1458.318.1r2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[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, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]]]}
  • id: 14267875
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 35, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 243, 'label': '1458.318.1s1', 'nt': [6, 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, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 14267876
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  • id: 14267877
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  • id: 14267878
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  • id: 14267879
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  • id: 14267881
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  • id: 14267882
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  • id: 14267883
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  • id: 14267884
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  • id: 14267885
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  • id: 14267886
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  • id: 14267887
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 46, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 243, 'label': '1458.318.1x2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 14267888
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  • id: 14267889
    {'center': '1.a1', 'center_index': 1, 'center_order': 1458, 'counter': 48, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 243, 'label': '1458.318.1y2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 14267890
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  • id: 14267892
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  • id: 14267897
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  • id: 14267898
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  • id: 14267899
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  • id: 14267900
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  • id: 14267901
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  • id: 14267903
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  • id: 14267904
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  • id: 14267905
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  • id: 14267906
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  • id: 14267907
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  • id: 14267908
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  • id: 14267909
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  • id: 14267910
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  • id: 14267911
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  • id: 14267912
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  • id: 14267914
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  • id: 14267915
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  • id: 14267916
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  • id: 14267917
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  • id: 14267918
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  • id: 14267919
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  • id: 14267920
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  • id: 14267921
    {'center': '9.c1', 'center_index': 9, 'center_order': 162, 'counter': 77, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.e1', 'kernel_order': 54, 'label': '1458.318.3l1', 'nt': [9, 7], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[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]], [[3, 0]], [[3, 1]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 1]], [[0, 0]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267922
    {'center': '9.c1', 'center_index': 9, 'center_order': 162, 'counter': 78, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.e1', 'kernel_order': 54, 'label': '1458.318.3l2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[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]], [[3, 0]], [[3, -1]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, -1]], [[0, 0]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267923
    {'center': '9.b1', 'center_index': 9, 'center_order': 162, 'counter': 79, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.d1', 'kernel_order': 27, 'label': '1458.318.3m1', 'nt': [18, 15], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267925
    {'center': '9.b1', 'center_index': 9, 'center_order': 162, 'counter': 80, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.d1', 'kernel_order': 27, 'label': '1458.318.3m2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267926
    {'center': '9.b1', 'center_index': 9, 'center_order': 162, 'counter': 81, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.d1', 'kernel_order': 27, 'label': '1458.318.3n1', 'nt': [18, 15], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267927
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  • id: 14267928
    {'center': '9.b1', 'center_index': 9, 'center_order': 162, 'counter': 83, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.c1', 'kernel_order': 27, 'label': '1458.318.3o1', 'nt': [18, 15], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267929
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  • id: 14267930
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  • id: 14267931
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  • id: 14267932
    {'center': '9.c1', 'center_index': 9, 'center_order': 162, 'counter': 87, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.e1', 'kernel_order': 27, 'label': '1458.318.3q1', 'nt': [18, 15], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 0]], [[3, -1]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[-3, -1]], [[0, 0]], [[-3, -1]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267933
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  • id: 14267934
    {'center': '9.c1', 'center_index': 9, 'center_order': 162, 'counter': 89, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.e1', 'kernel_order': 27, 'label': '1458.318.3r1', 'nt': [18, 15], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 1]], [[3, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[-3, 1]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267936
    {'center': '9.c1', 'center_index': 9, 'center_order': 162, 'counter': 90, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.e1', 'kernel_order': 27, 'label': '1458.318.3r2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, -1]], [[3, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[-3, -1]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267937
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  • id: 14267938
    {'center': '9.a1', 'center_index': 9, 'center_order': 162, 'counter': 92, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1', 'kernel_order': 27, 'label': '1458.318.3s2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 1]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, 1]], [[-3, 0]], [[-3, 1]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 14267939
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  • id: 14267940
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  • id: 14267941
    {'center': '9.a1', 'center_index': 9, 'center_order': 162, 'counter': 95, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1', 'kernel_order': 27, 'label': '1458.318.3u1', 'nt': [18, 15], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, 1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, -1]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 14267942
    {'center': '9.a1', 'center_index': 9, 'center_order': 162, 'counter': 96, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.b1', 'kernel_order': 27, 'label': '1458.318.3u2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, -1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, 1]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 14267943
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  • id: 14267944
    {'center': '9.c1', 'center_index': 9, 'center_order': 162, 'counter': 98, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.e1', 'kernel_order': 27, 'label': '1458.318.3v2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-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]], [[3, 1]], [[3, 1]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267945
    {'center': '9.c1', 'center_index': 9, 'center_order': 162, 'counter': 99, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.e1', 'kernel_order': 27, 'label': '1458.318.3w1', 'nt': [18, 15], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-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]], [[3, 1]], [[3, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, -1]], [[0, 0]], [[-3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267834
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  • id: 14267835
    {'center': '9.c1', 'center_index': 9, 'center_order': 162, 'counter': 101, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '54.10', 'image_order': 54, 'indicator': 0, 'kernel': '54.e1', 'kernel_order': 27, 'label': '1458.318.3x1', 'nt': [18, 15], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-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]], [[3, 0]], [[3, 1]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, 1]], [[0, 0]], [[-3, -1]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 14267836
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  • id: 14267837
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  • id: 14267838
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  • id: 14267839
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  • id: 14267840
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  • id: 14267841
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  • id: 14267842
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  • id: 14267843
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  • id: 14267845
    {'center': '243.a1', 'center_index': 243, 'center_order': 6, 'counter': 110, 'cyclotomic_n': 9, 'dim': 9, 'faithful': True, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '1458.318', 'image_order': 1458, 'indicator': 0, 'kernel': '1458.a1', 'kernel_order': 1, 'label': '1458.318.9b2', 'nt': [162, 6], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[9, 3]], [[9, -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]], [[-9, -3]], [[-9, 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]], [[3, 1], [6, 4]], [[-3, 2], [3, -4]], [[-3, 2], [-6, -4]], [[3, 1], [-3, 4]], [[-6, 1], [-3, 4]], [[6, 2], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [6, -4]], [[-6, 2], [-3, -4]], [[-3, 1], [-6, 4]], [[6, 1], [3, 4]], [[-3, 1], [3, 4]], [[3, 2], [-3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 14267846
    {'center': '243.a1', 'center_index': 243, 'center_order': 6, 'counter': 111, 'cyclotomic_n': 9, 'dim': 9, 'faithful': True, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '1458.318', 'image_order': 1458, 'indicator': 0, 'kernel': '1458.a1', 'kernel_order': 1, 'label': '1458.318.9b3', 'nt': [162, 0], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[9, -3]], [[9, 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]], [[-9, 3]], [[-9, -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]], [[6, 2], [3, -4]], [[-6, 1], [-3, 4]], [[3, 1], [6, 4]], [[-3, 2], [3, -4]], [[-3, 2], [-6, -4]], [[3, 1], [-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [-6, 4]], [[-3, 1], [3, 4]], [[-6, 2], [-3, -4]], [[3, 2], [6, -4]], [[3, 2], [-3, -4]], [[6, 1], [3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 14267847
    {'center': '243.a1', 'center_index': 243, 'center_order': 6, 'counter': 112, 'cyclotomic_n': 9, 'dim': 9, 'faithful': True, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '1458.318', 'image_order': 1458, 'indicator': 0, 'kernel': '1458.a1', 'kernel_order': 1, 'label': '1458.318.9b4', 'nt': [162, 6], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[9, 3]], [[9, -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]], [[-9, -3]], [[-9, 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]], [[-6, 1], [-3, 4]], [[6, 2], [3, -4]], [[-3, 2], [3, -4]], [[3, 1], [6, 4]], [[3, 1], [-3, 4]], [[-3, 2], [-6, -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, 0]], [[0, 0]], [[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, 2], [-3, -4]], [[3, 2], [6, -4]], [[6, 1], [3, 4]], [[-3, 1], [3, 4]], [[-3, 1], [-6, 4]], [[-6, 2], [-3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 14267848
    {'center': '243.a1', 'center_index': 243, 'center_order': 6, 'counter': 113, 'cyclotomic_n': 9, 'dim': 9, 'faithful': True, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '1458.318', 'image_order': 1458, 'indicator': 0, 'kernel': '1458.a1', 'kernel_order': 1, 'label': '1458.318.9b5', 'nt': [162, 0], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[9, -3]], [[9, 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]], [[-9, 3]], [[-9, -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]], [[-3, 2], [-6, -4]], [[3, 1], [-3, 4]], [[-6, 1], [-3, 4]], [[6, 2], [3, -4]], [[-3, 2], [3, -4]], [[3, 1], [6, 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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1], [3, 4]], [[-3, 1], [-6, 4]], [[3, 2], [6, -4]], [[3, 2], [-3, -4]], [[-6, 2], [-3, -4]], [[-3, 1], [3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 14267849
    {'center': '243.a1', 'center_index': 243, 'center_order': 6, 'counter': 114, 'cyclotomic_n': 9, 'dim': 9, 'faithful': True, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1458.318', 'group_counter': 318, 'group_order': 1458, 'image': None, 'image_isoclass': '1458.318', 'image_order': 1458, 'indicator': 0, 'kernel': '1458.a1', 'kernel_order': 1, 'label': '1458.318.9b6', 'nt': [162, 6], 'q_character': None, 'values': [[[9, 0]], [[-9, 0]], [[9, 3]], [[9, -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]], [[-9, -3]], [[-9, 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]], [[3, 1], [-3, 4]], [[-3, 2], [-6, -4]], [[6, 2], [3, -4]], [[-6, 1], [-3, 4]], [[3, 1], [6, 4]], [[-3, 2], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 2], [-3, -4]], [[3, 2], [-3, -4]], [[-3, 1], [3, 4]], [[-3, 1], [-6, 4]], [[6, 1], [3, 4]], [[3, 2], [6, -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, 0]], [[0, 0]], [[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 •

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

  
  
  • id: 76312230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1458, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1458.318.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1458.318', 'subgroup_hash': 318, 'subgroup_order': 1458, 'subgroup_tex': 'C_2\\times C_3^3.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 729, 'counter': 2, 'cyclic': False, 'direct': True, 'hall': 3, 'label': '1458.318.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, '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': '729.318', 'subgroup_hash': 318, 'subgroup_order': 729, 'subgroup_tex': 'C_3^3.C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 76312271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 486, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.253', 'subgroup_hash': 253, 'subgroup_order': 486, 'subgroup_tex': 'C_{18}.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 486, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.3.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.b1', 'outer_equivalence': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.216', 'subgroup_hash': 216, 'subgroup_order': 486, 'subgroup_tex': '(C_3\\times C_{18}):C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 486, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.3.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.c1', 'outer_equivalence': True, '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': '486.213', 'subgroup_hash': 213, 'subgroup_order': 486, 'subgroup_tex': 'C_3\\times C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 486, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.3.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.d1', 'outer_equivalence': True, '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': '486.213', 'subgroup_hash': 213, 'subgroup_order': 486, 'subgroup_tex': 'C_3\\times C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 486, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.3.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.e1', 'outer_equivalence': True, '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': '486.218', 'subgroup_hash': 218, 'subgroup_order': 486, 'subgroup_tex': 'C_2\\times C_3^2.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 243, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '243.64', 'subgroup_hash': 64, 'subgroup_order': 243, 'subgroup_tex': 'C_9.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 243, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '243.57', 'subgroup_hash': 57, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 243, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.54', 'subgroup_hash': 54, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 243, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.54', 'subgroup_hash': 54, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 243, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.59', 'subgroup_hash': 59, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 162, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.48', 'subgroup_hash': 48, 'subgroup_order': 162, 'subgroup_tex': 'C_6\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312254
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 162, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.47', 'subgroup_hash': 47, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 162, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.9.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.9.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.f1', 'outer_equivalence': True, 'perfect': False, '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': '162.50', 'subgroup_hash': 50, 'subgroup_order': 162, 'subgroup_tex': 'C_6.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.g1', 'outer_equivalence': True, 'perfect': False, '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': '162.29', 'subgroup_hash': 29, 'subgroup_order': 162, 'subgroup_tex': 'C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312261
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 54, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.h1', 'outer_equivalence': True, 'perfect': False, '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': '162.47', 'subgroup_hash': 47, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.i1', 'outer_equivalence': True, 'perfect': False, '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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.j1', 'outer_equivalence': True, 'perfect': False, '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': '162.31', 'subgroup_hash': 31, 'subgroup_order': 162, 'subgroup_tex': 'C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.k1', 'outer_equivalence': True, 'perfect': False, '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': '162.31', 'subgroup_hash': 31, 'subgroup_order': 162, 'subgroup_tex': 'C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.l1', 'outer_equivalence': True, 'perfect': False, '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': '162.31', 'subgroup_hash': 31, 'subgroup_order': 162, 'subgroup_tex': 'C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.m1', 'outer_equivalence': True, 'perfect': False, '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': '162.31', 'subgroup_hash': 31, 'subgroup_order': 162, 'subgroup_tex': 'C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.n1', 'outer_equivalence': True, 'perfect': False, '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': '162.50', 'subgroup_hash': 50, 'subgroup_order': 162, 'subgroup_tex': 'C_6.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.9.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.o1', 'outer_equivalence': True, 'perfect': False, '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': '162.31', 'subgroup_hash': 31, 'subgroup_order': 162, 'subgroup_tex': 'C_6.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 81, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 81, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 81, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, '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': '81.14', 'subgroup_hash': 14, 'subgroup_order': 81, 'subgroup_tex': 'C_9.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, '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': '81.8', 'subgroup_hash': 8, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312277
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 27, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, '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': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, '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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, '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': '81.10', 'subgroup_hash': 10, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, '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': '81.10', 'subgroup_hash': 10, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, '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': '81.10', 'subgroup_hash': 10, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, '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': '81.10', 'subgroup_hash': 10, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, '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': '81.14', 'subgroup_hash': 14, 'subgroup_order': 81, 'subgroup_tex': 'C_9.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, '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': '81.10', 'subgroup_hash': 10, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312286
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 54, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312288
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 54, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312289
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 54, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.27.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.27.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312294
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312296
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312297
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312301
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312305
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.r2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.r2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312307
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.27.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312309
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 27, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312311
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 27, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312312
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 27, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312314
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312317
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312319
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 76312320
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312324
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312328
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.r2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.r2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312330
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.54.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 18, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '81.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 81, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 18, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '81.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 81, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 18, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.81.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '81.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '81.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 81, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.81.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.d1', 'outer_equivalence': True, 'perfect': False, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312336
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 6, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.81.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.e1', 'outer_equivalence': True, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312338
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.81.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.f1', 'outer_equivalence': True, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312339
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 91, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.81.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.g1', 'outer_equivalence': True, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312340
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 92, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.81.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.h1', 'outer_equivalence': True, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312341
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 93, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.81.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.i1', 'outer_equivalence': True, 'perfect': False, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 76312342
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.81.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.j1', 'outer_equivalence': True, 'perfect': False, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.81.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.k1', 'outer_equivalence': True, 'perfect': False, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 9, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '162.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 9, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '162.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 9, 'counter': 98, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1458.318.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '162.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.d1', 'outer_equivalence': True, 'perfect': False, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312232
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.e1', 'outer_equivalence': True, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312233
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.162.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.f1', 'outer_equivalence': True, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312234
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.162.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.g1', 'outer_equivalence': True, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312235
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.162.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.h1', 'outer_equivalence': True, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312236
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.162.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.i1', 'outer_equivalence': True, 'perfect': False, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 76312237
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.162.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.j1', 'outer_equivalence': True, 'perfect': False, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312238
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1458.318.162.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.k1', 'outer_equivalence': True, 'perfect': False, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 76312239
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': True, 'core_order': 6, 'counter': 107, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1458.318.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '243.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 243, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^4:C_3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312240
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 2, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.243.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312241
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.243.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312243
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.243.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312244
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.243.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 76312245
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': True, 'core_order': 3, 'counter': 112, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1458.318.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '486.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '486.196', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 196, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 486, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^4:C_6', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312246
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312247
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.486.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312248
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.486.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312249
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1458.318.486.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 76312250
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': True, 'core_order': 2, 'counter': 117, 'cyclic': True, 'direct': True, 'hall': 2, 'label': '1458.318.729.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '729.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '729.318', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 318, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 729, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3.C_3^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 2}
  • id: 76312251
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1458.318', 'ambient_counter': 318, 'ambient_order': 1458, 'ambient_tex': 'C_2\\times C_3^3.C_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': True, 'core_order': 1, 'counter': 118, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1458.318.1458.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1458.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1458.318', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 318, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1458, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_3^3.C_3^3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 76312248
    {'ambient': '1458.318', 'aut_centralizer_order': 13122, 'aut_label': '486.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 78732, 'centralizer': '3.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.c1', '162.j1', '243.d1'], 'contains': ['1458.a1'], 'core': '1458.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6234, -1, 5580, -1], 'generators': [1008], 'label': '1458.318.486.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '486.d1', 'projective_image': '1458.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312249
    {'ambient': '1458.318', 'aut_centralizer_order': 1458, 'aut_label': '486.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 39366, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['162.d1', '162.k1', '243.e1'], 'contains': ['1458.a1'], 'core': '1458.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3896, -1, 2253, -1], 'generators': [1], 'label': '1458.318.486.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.h1', 'old_label': '486.e1', 'projective_image': '1458.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312230
    {'ambient': '1458.318', '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': '243.a1', 'complements': ['1458.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '3.a1', '3.b1', '3.c1', '3.d1', '3.e1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5959, 5676, 6926, 5750], 'generators': [729, 999, 9, 1, 486, 3, 162], 'label': '1458.318.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '3.a1', '3.b1', '3.c1', '3.d1', '3.e1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '243.37'}
  • id: 76312231
    {'ambient': '1458.318', 'aut_centralizer_order': 9, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '81.a1', 'complements': ['243.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.c1'], 'contains': ['18.b1', '18.d1', '18.j1', '18.l1'], 'core': '6.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4283, 7970, 6064, 7351], 'generators': [3, 162, 999], 'label': '1458.318.6.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1', 'normal_contained_in': ['2.a1', '3.c1'], 'normal_contains': ['18.b1', '18.d1'], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': '486.196', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312232
    {'ambient': '1458.318', 'aut_centralizer_order': 4374, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1', '54.f1', '54.o1', '54.s1', '81.e1'], 'contains': ['486.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2668, -1, 4382, -1], 'generators': [162], 'label': '1458.318.162.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '162.e1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312233
    {'ambient': '1458.318', 'aut_centralizer_order': 2187, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.d1', '54.f1', '54.o1', '54.t1', '81.f1'], 'contains': ['486.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2400, -1, 4044, -1], 'generators': [1161], 'label': '1458.318.162.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '162.f1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312234
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['54.e1', '54.g1', '54.k1', '54.p1', '54.s1', '54.t1', '81.g1'], 'contains': ['486.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4751, -1, 2931, -1], 'generators': [163], 'label': '1458.318.162.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '162.g1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312235
    {'ambient': '1458.318', 'aut_centralizer_order': 486, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '27.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['54.h1', '54.l1', '54.q1', '81.h1'], 'contains': ['486.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5846, -1, 6643, -1], 'generators': [3], 'label': '1458.318.162.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '162.h1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312236
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '162.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '27.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['54.i1', '54.m1', '54.r1', '54.r2', '81.i1'], 'contains': ['486.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8693, -1, 8338, -1], 'generators': [544], 'label': '1458.318.162.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.e1', 'old_label': '162.i1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.i1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312237
    {'ambient': '1458.318', 'aut_centralizer_order': 4374, 'aut_label': '162.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 39366, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '81.j1'], 'contains': ['486.b1', '486.c1', '486.d1'], 'core': '1458.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6183, -1, 5714, -1], 'generators': [495, 999], 'label': '1458.318.162.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '162.j1', 'projective_image': '1458.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312238
    {'ambient': '1458.318', 'aut_centralizer_order': 486, 'aut_label': '162.k1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13122, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['54.j1', '81.k1'], 'contains': ['486.c1', '486.e1'], 'core': '1458.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3968, -1, 1873, -1], 'generators': [1, 495], 'label': '1458.318.162.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.h1', 'old_label': '162.k1', 'projective_image': '1458.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312239
    {'ambient': '1458.318', 'aut_centralizer_order': 39366, 'aut_label': '243.a1', 'aut_quo_index': 216, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 39366, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1', '81.c1', '81.d1', '81.e1', '81.f1', '81.g1', '81.h1', '81.i1'], 'contains': ['486.a1', '729.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4724, 4853, 5168, 4558], 'generators': [729, 486], 'label': '1458.318.243.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '243.a1', 'normal_contained_in': ['81.a1', '81.b1', '81.c1'], 'normal_contains': ['486.a1', '729.a1'], 'normalizer': '1.a1', 'old_label': '243.a1', 'projective_image': '243.37', 'quotient_action_image': '1.1', 'quotient_action_kernel': '243.37', 'quotient_action_kernel_order': 243, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312240
    {'ambient': '1458.318', 'aut_centralizer_order': 13122, 'aut_label': '243.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 39366, 'centralizer': '3.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.j1'], 'contains': ['486.b1', '729.a1'], 'core': '729.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5425, -1, 5580, -1], 'generators': [729, 999], 'label': '1458.318.243.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '81.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '243.b1', 'projective_image': '729.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312241
    {'ambient': '1458.318', 'aut_centralizer_order': 26244, 'aut_label': '243.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 78732, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.b1', '81.j1', '81.k1'], 'contains': ['486.c1', '729.a1'], 'core': '729.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4596, -1, 4900, -1], 'generators': [729, 495], 'label': '1458.318.243.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '81.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '243.c1', 'projective_image': '729.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312242
    {'ambient': '1458.318', 'aut_centralizer_order': 9, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '81.c1', 'complements': ['243.e1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.d1'], 'contains': ['18.b1', '18.e1', '18.k1', '18.m1'], 'core': '6.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [6640, 5484, 8282, 8512], 'generators': [544, 162, 999], 'label': '1458.318.6.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1', 'normal_contained_in': ['2.a1', '3.d1'], 'normal_contains': ['18.b1', '18.e1'], 'normalizer': '1.a1', 'old_label': '6.d1', 'projective_image': '486.196', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312243
    {'ambient': '1458.318', 'aut_centralizer_order': 13122, 'aut_label': '243.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 78732, 'centralizer': '3.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['81.c1', '81.j1'], 'contains': ['486.d1', '729.a1'], 'core': '729.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6286, -1, 5869, -1], 'generators': [729, 1008], 'label': '1458.318.243.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '81.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '243.d1', 'projective_image': '729.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312244
    {'ambient': '1458.318', 'aut_centralizer_order': 1458, 'aut_label': '243.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 39366, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['81.d1', '81.k1'], 'contains': ['486.e1', '729.a1'], 'core': '729.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3684, -1, 2166, -1], 'generators': [729, 1], 'label': '1458.318.243.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.h1', 'old_label': '243.e1', 'projective_image': '729.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312245
    {'ambient': '1458.318', 'aut_centralizer_order': 39366, 'aut_label': '486.a1', 'aut_quo_index': 216, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 39366, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['162.a1', '162.b1', '162.c1', '162.d1', '162.e1', '162.f1', '162.g1', '162.h1', '162.i1', '243.a1'], 'contains': ['1458.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4947, 4523, 5051, 4185], 'generators': [486], 'label': '1458.318.486.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '486.a1', 'normal_contained_in': ['162.a1', '162.b1', '162.c1', '243.a1'], 'normal_contains': ['1458.a1'], 'normalizer': '1.a1', 'old_label': '486.a1', 'projective_image': '486.196', 'quotient_action_image': '1.1', 'quotient_action_kernel': '486.196', 'quotient_action_kernel_order': 486, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312246
    {'ambient': '1458.318', 'aut_centralizer_order': 13122, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 39366, 'centralizer': '3.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1', '162.j1', '243.b1'], 'contains': ['1458.a1'], 'core': '1458.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5366, -1, 5311, -1], 'generators': [999], 'label': '1458.318.486.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '486.b1', 'projective_image': '1458.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312247
    {'ambient': '1458.318', 'aut_centralizer_order': 26244, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 78732, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.b1', '162.j1', '162.k1', '243.c1'], 'contains': ['1458.a1'], 'core': '1458.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4821, -1, 4926, -1], 'generators': [495], 'label': '1458.318.486.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '486.c1', 'projective_image': '1458.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312250
    {'ambient': '1458.318', 'aut_centralizer_order': 78732, 'aut_label': '729.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 78732, 'centralizer': '1.a1', 'complements': ['2.a1'], 'conjugacy_class_count': 1, 'contained_in': ['243.a1', '243.b1', '243.c1', '243.d1', '243.e1'], 'contains': ['1458.a1'], 'core': '729.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4731, 4853, 5177, 4558], 'generators': [729], 'label': '1458.318.729.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '729.a1', 'normal_contained_in': ['243.a1'], 'normal_contains': ['1458.a1'], 'normalizer': '1.a1', 'old_label': '729.a1', 'projective_image': '729.318', 'quotient_action_image': '1.1', 'quotient_action_kernel': '729.318', 'quotient_action_kernel_order': 729, 'quotient_fusion': None, 'short_label': '729.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312251
    {'ambient': '1458.318', 'aut_centralizer_order': None, 'aut_label': '1458.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['486.a1', '486.b1', '486.c1', '486.d1', '486.e1', '729.a1'], 'contains': [], 'core': '1458.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4877, 4692, 5114, 4371], 'generators': [], 'label': '1458.318.1458.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1458.a1', 'normal_contained_in': ['486.a1', '729.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1458.a1', 'projective_image': '1458.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312252
    {'ambient': '1458.318', 'aut_centralizer_order': 3, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '243.a1', 'complements': ['243.e1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '3.e1'], 'contains': ['18.c1', '18.d1', '18.e1', '18.o1'], 'core': '6.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [7312, 2006, 7492, 3402], 'generators': [163, 3, 999], 'label': '1458.318.6.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1', 'normal_contained_in': ['2.a1', '3.e1'], 'normal_contains': ['18.c1', '18.d1', '18.e1'], 'normalizer': '1.a1', 'old_label': '6.e1', 'projective_image': '486.196', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '243.37'}
  • id: 76312253
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '9.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '972.811', 'aut_weyl_index': 81, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.a1', '27.a1', '27.b1', '27.j1', '27.n1'], 'core': '9.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5155, 3496, 2675, 1319], 'generators': [729, 486, 1, 9, 999], 'label': '1458.318.9.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.a1', 'normal_contained_in': ['3.a1', '3.b1'], 'normal_contains': ['18.a1', '27.a1', '27.b1'], 'normalizer': '1.a1', 'old_label': '9.a1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312254
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '9.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '108.38', 'aut_weyl_index': 729, 'centralizer': '9.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.c1', '3.d1'], 'contains': ['18.b1', '27.a1', '27.c1', '27.d1', '27.f1', '27.o1'], 'core': '9.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1899, 7994, 4928, 9570], 'generators': [729, 486, 162, 9, 999], 'label': '1458.318.9.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.b1', 'normal_contained_in': ['3.a1', '3.c1', '3.d1'], 'normal_contains': ['18.b1', '27.a1', '27.c1', '27.d1'], 'normalizer': '1.a1', 'old_label': '9.b1', 'projective_image': '243.37', 'quotient_action_image': '9.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312255
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '9.c1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '486.249', 'aut_weyl_index': 162, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '3.e1'], 'contains': ['18.c1', '27.a1', '27.e1', '27.g1', '27.k1', '27.p1'], 'core': '9.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6010, 1273, 3730, 386], 'generators': [729, 486, 163, 9, 999], 'label': '1458.318.9.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.c1', 'normal_contained_in': ['3.a1', '3.e1'], 'normal_contains': ['18.c1', '27.a1', '27.e1'], 'normalizer': '1.a1', 'old_label': '9.c1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312256
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '9.d1', 'aut_quo_index': 12, 'aut_stab_index': 3, 'aut_weyl_group': '972.812', 'aut_weyl_index': 81, 'centralizer': '81.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['3.b1', '3.c1', '3.e1'], 'contains': ['18.d1', '27.a1', '27.h1', '27.l1', '27.q1'], 'core': '9.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [6505, 6487, 6406, 4444], 'generators': [729, 486, 3, 9, 999], 'label': '1458.318.9.d1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.d1', 'normal_contained_in': ['3.b1', '3.c1', '3.e1'], 'normal_contains': ['18.d1', '27.a1'], 'normalizer': '1.a1', 'old_label': '9.d1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312257
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '9.e1', 'aut_quo_index': 24, 'aut_stab_index': 6, 'aut_weyl_group': '486.249', 'aut_weyl_index': 162, 'centralizer': '81.c1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['3.b1', '3.d1', '3.e1'], 'contains': ['18.e1', '27.a1', '27.i1', '27.m1', '27.r1', '27.r2'], 'core': '9.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [8128, 5262, 9405, 5310], 'generators': [729, 486, 544, 9, 999], 'label': '1458.318.9.e1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.e1', 'normal_contained_in': ['3.b1', '3.d1', '3.e1'], 'normal_contains': ['18.e1', '27.a1'], 'normalizer': '1.a1', 'old_label': '9.e1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312258
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '324.117', 'aut_weyl_index': 243, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1'], 'contains': ['18.f1', '27.b1', '27.f1', '27.g1', '27.s1', '27.t1'], 'core': '27.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [2524, -1, 2025, -1], 'generators': [729, 486, 1, 162, 999], 'label': '1458.318.9.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.f1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312259
    {'ambient': '1458.318', 'aut_centralizer_order': 9, 'aut_label': '9.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '324.117', 'aut_weyl_index': 243, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['3.b1'], 'contains': ['18.g1', '27.b1', '27.h1', '27.i1'], 'core': '27.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [5598, -1, 6748, -1], 'generators': [729, 486, 1, 3, 999], 'label': '1458.318.9.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.g1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.g1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312260
    {'ambient': '1458.318', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '243.a1', 'complements': ['729.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1', '6.e1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6035, 3946, 7105, 6279], 'generators': [1, 3, 162], 'label': '1458.318.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.a1', '6.b1', '6.c1', '6.d1', '6.e1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '486.196', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '243.37'}
  • id: 76312261
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '9.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '324.117', 'aut_weyl_index': 243, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.h1', '27.c1', '27.j1', '27.k1', '27.s1'], 'core': '27.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [2921, -1, 1594, -1], 'generators': [729, 486, 1, 162, 9], 'label': '1458.318.9.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.h1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312262
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '9.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '162.34', 'aut_weyl_index': 486, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1'], 'contains': ['18.i1', '27.d1', '27.j1', '27.k1', '27.t1'], 'core': '27.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [2211, -1, 1075, -1], 'generators': [729, 486, 1, 1161, 9], 'label': '1458.318.9.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.i1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.i1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312263
    {'ambient': '1458.318', 'aut_centralizer_order': 54, 'aut_label': '9.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '486.130', 'aut_weyl_index': 162, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['18.j1', '27.c1', '27.l1'], 'core': '27.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [1538, -1, 5674, -1], 'generators': [729, 486, 3, 162, 9], 'label': '1458.318.9.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '9.j1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.j1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312264
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '9.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '486.130', 'aut_weyl_index': 162, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.d1'], 'contains': ['18.k1', '27.c1', '27.m1'], 'core': '27.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7515, -1, 8672, -1], 'generators': [729, 486, 544, 162, 9], 'label': '1458.318.9.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '9.k1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.k1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312265
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '9.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '486.130', 'aut_weyl_index': 162, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.c1'], 'contains': ['18.l1', '27.d1', '27.l1'], 'core': '27.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [869, -1, 5283, -1], 'generators': [729, 486, 543, 1161, 9], 'label': '1458.318.9.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '9.l1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.l1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312266
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '9.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '243.58', 'aut_weyl_index': 324, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.d1'], 'contains': ['18.m1', '27.d1', '27.m1'], 'core': '27.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [6984, -1, 7891, -1], 'generators': [729, 486, 1003, 1161, 981], 'label': '1458.318.9.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '9.m1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.m1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312267
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '9.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '162.41', 'aut_weyl_index': 486, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['3.a1'], 'contains': ['18.n1', '27.e1', '27.n1', '27.o1', '27.p1', '27.s1', '27.t1'], 'core': '27.e1', 'coset_action_label': None, 'count': 18, 'diagramx': [3250, -1, 3336, -1], 'generators': [729, 486, 1, 162, 1008], 'label': '1458.318.9.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.n1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.n1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312268
    {'ambient': '1458.318', 'aut_centralizer_order': 9, 'aut_label': '9.o1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '162.41', 'aut_weyl_index': 486, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['3.e1'], 'contains': ['18.o1', '27.e1', '27.q1', '27.r1', '27.r2'], 'core': '27.e1', 'coset_action_label': None, 'count': 54, 'diagramx': [8605, -1, 9063, -1], 'generators': [729, 486, 163, 3, 549], 'label': '1458.318.9.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '9.o1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.o1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312269
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '18.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '972.811', 'aut_weyl_index': 81, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.b1', '9.a1'], 'contains': ['54.a1', '54.b1', '54.j1', '54.n1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5155, 2570, 2675, 3537], 'generators': [1, 9, 999], 'label': '1458.318.18.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1', '6.b1', '9.a1'], 'normal_contains': ['54.a1', '54.b1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312270
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '18.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '108.38', 'aut_weyl_index': 729, 'centralizer': '9.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.c1', '6.d1', '9.b1'], 'contains': ['54.a1', '54.c1', '54.d1', '54.f1', '54.o1'], 'core': '18.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4440, 6769, 5524, 6989], 'generators': [162, 9, 999], 'label': '1458.318.18.b1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1', 'normal_contained_in': ['6.a1', '6.c1', '6.d1', '9.b1'], 'normal_contains': ['54.a1', '54.c1', '54.d1'], 'normalizer': '1.a1', 'old_label': '18.b1', 'projective_image': '486.196', 'quotient_action_image': '9.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312271
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 27, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '9.a1', '9.b1', '9.c1', '9.f1', '9.h1', '9.i1', '9.n1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3250, 2498, 3008, 2309], 'generators': [729, 486, 999, 1, 162, 9], 'label': '1458.318.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.a1', '9.a1', '9.b1', '9.c1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312272
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '18.c1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '486.249', 'aut_weyl_index': 162, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.e1', '9.c1'], 'contains': ['54.a1', '54.e1', '54.g1', '54.k1', '54.p1'], 'core': '18.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6258, 1261, 3522, 2604], 'generators': [163, 9, 999], 'label': '1458.318.18.c1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1', 'normal_contained_in': ['6.a1', '6.e1', '9.c1'], 'normal_contains': ['54.a1', '54.e1'], 'normalizer': '1.a1', 'old_label': '18.c1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312273
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '18.d1', 'aut_quo_index': 12, 'aut_stab_index': 3, 'aut_weyl_group': '972.812', 'aut_weyl_index': 81, 'centralizer': '81.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.c1', '6.e1', '9.d1'], 'contains': ['54.a1', '54.h1', '54.l1', '54.q1'], 'core': '18.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [6820, 5340, 7175, 5284], 'generators': [3, 9, 999], 'label': '1458.318.18.d1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.d1', 'normal_contained_in': ['6.b1', '6.c1', '6.e1', '9.d1'], 'normal_contains': ['54.a1'], 'normalizer': '1.a1', 'old_label': '18.d1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312274
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '18.e1', 'aut_quo_index': 24, 'aut_stab_index': 6, 'aut_weyl_group': '486.249', 'aut_weyl_index': 162, 'centralizer': '81.c1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['6.b1', '6.d1', '6.e1', '9.e1'], 'contains': ['54.a1', '54.i1', '54.m1', '54.r1', '54.r2'], 'core': '18.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [7908, 4337, 9004, 6149], 'generators': [544, 9, 999], 'label': '1458.318.18.e1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.e1', 'normal_contained_in': ['6.b1', '6.d1', '6.e1', '9.e1'], 'normal_contains': ['54.a1'], 'normalizer': '1.a1', 'old_label': '18.e1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312275
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '324.117', 'aut_weyl_index': 243, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.a1', '9.f1'], 'contains': ['54.b1', '54.f1', '54.g1', '54.s1', '54.t1'], 'core': '54.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [2613, -1, 1497, -1], 'generators': [1, 162, 999], 'label': '1458.318.18.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.f1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312276
    {'ambient': '1458.318', 'aut_centralizer_order': 9, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '324.117', 'aut_weyl_index': 243, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['6.b1', '9.g1'], 'contains': ['54.b1', '54.h1', '54.i1'], 'core': '54.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [5819, -1, 7700, -1], 'generators': [1, 3], 'label': '1458.318.18.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.g1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312277
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '324.117', 'aut_weyl_index': 243, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.h1'], 'contains': ['54.c1', '54.j1', '54.k1', '54.s1'], 'core': '54.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [3900, -1, 686, -1], 'generators': [1, 162, 9], 'label': '1458.318.18.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.h1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312278
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '162.34', 'aut_weyl_index': 486, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '9.i1'], 'contains': ['54.d1', '54.j1', '54.k1', '54.t1'], 'core': '54.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [3350, -1, 404, -1], 'generators': [1, 1161, 9], 'label': '1458.318.18.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.i1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312279
    {'ambient': '1458.318', 'aut_centralizer_order': 54, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '486.130', 'aut_weyl_index': 162, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '9.j1'], 'contains': ['54.c1', '54.l1'], 'core': '54.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4171, -1, 6615, -1], 'generators': [3, 162], 'label': '1458.318.18.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.j1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312280
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '486.130', 'aut_weyl_index': 162, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '9.k1'], 'contains': ['54.c1', '54.m1'], 'core': '54.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7472, -1, 8177, -1], 'generators': [544, 162], 'label': '1458.318.18.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '18.k1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312281
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '486.130', 'aut_weyl_index': 162, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '9.l1'], 'contains': ['54.d1', '54.l1'], 'core': '54.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [3629, -1, 6064, -1], 'generators': [3, 1161], 'label': '1458.318.18.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.l1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312282
    {'ambient': '1458.318', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '8748.nx', 'aut_weyl_index': 9, 'centralizer': '243.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['6.b1', '9.a1', '9.d1', '9.e1', '9.g1'], 'core': '3.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5789, 6420, 6748, 5221], 'generators': [729, 486, 999, 1, 3, 9], 'label': '1458.318.3.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.b1', '9.a1', '9.d1', '9.e1'], 'normalizer': '1.a1', 'old_label': '3.b1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '243.37'}
  • id: 76312283
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '243.58', 'aut_weyl_index': 324, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '9.m1'], 'contains': ['54.d1', '54.m1'], 'core': '54.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [7166, -1, 7917, -1], 'generators': [544, 1161], 'label': '1458.318.18.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '18.m1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312284
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '162.41', 'aut_weyl_index': 486, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.a1', '9.n1'], 'contains': ['54.e1', '54.n1', '54.o1', '54.p1', '54.s1', '54.t1'], 'core': '54.e1', 'coset_action_label': None, 'count': 18, 'diagramx': [3035, -1, 3278, -1], 'generators': [1, 162, 1008], 'label': '1458.318.18.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.n1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312285
    {'ambient': '1458.318', 'aut_centralizer_order': 9, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '162.41', 'aut_weyl_index': 486, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['6.e1', '9.o1'], 'contains': ['54.e1', '54.q1', '54.r1', '54.r2'], 'core': '54.e1', 'coset_action_label': None, 'count': 54, 'diagramx': [8703, -1, 8437, -1], 'generators': [163, 3], 'label': '1458.318.18.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '18.o1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312286
    {'ambient': '1458.318', 'aut_centralizer_order': 2187, 'aut_label': '27.a1', 'aut_quo_index': 936, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2187, 'centralizer': '9.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1', '9.c1', '9.d1', '9.e1'], 'contains': ['54.a1', '81.a1', '81.b1', '81.c1', '81.j1'], 'core': '27.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7038, 5196, 5798, 4444], 'generators': [729, 9, 999, 486], 'label': '1458.318.27.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '27.a1', 'normal_contained_in': ['9.a1', '9.b1', '9.c1', '9.d1', '9.e1'], 'normal_contains': ['54.a1', '81.a1', '81.b1', '81.c1'], 'normalizer': '1.a1', 'old_label': '27.a1', 'projective_image': '243.37', 'quotient_action_image': '9.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312287
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '27.b1', 'aut_quo_index': 8, 'aut_stab_index': 3, 'aut_weyl_group': '108.17', 'aut_weyl_index': 729, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['9.a1', '9.f1', '9.g1'], 'contains': ['54.b1', '81.a1', '81.d1'], 'core': '27.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5179, 3453, 2339, 1671], 'generators': [729, 1, 999, 486], 'label': '1458.318.27.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '27.b1', 'normal_contained_in': ['9.a1'], 'normal_contains': ['54.b1', '81.a1'], 'normalizer': '1.a1', 'old_label': '27.b1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312288
    {'ambient': '1458.318', 'aut_centralizer_order': 4374, 'aut_label': '27.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '18.3', 'aut_weyl_index': 4374, 'centralizer': '3.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '9.h1', '9.j1', '9.k1'], 'contains': ['54.c1', '81.b1', '81.e1'], 'core': '27.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1871, 7039, 5245, 8663], 'generators': [729, 162, 9, 486], 'label': '1458.318.27.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '27.c1', 'normal_contained_in': ['9.b1'], 'normal_contains': ['54.c1', '81.b1'], 'normalizer': '1.a1', 'old_label': '27.c1', 'projective_image': '243.37', 'quotient_action_image': '3.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312289
    {'ambient': '1458.318', 'aut_centralizer_order': 2187, 'aut_label': '27.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '18.3', 'aut_weyl_index': 4374, 'centralizer': '9.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['9.b1', '9.i1', '9.l1', '9.m1'], 'contains': ['54.d1', '81.b1', '81.f1'], 'core': '27.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [423, 8018, 4961, 7818], 'generators': [729, 1161, 9, 486], 'label': '1458.318.27.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '27.d1', 'normal_contained_in': ['9.b1'], 'normal_contains': ['54.d1', '81.b1'], 'normalizer': '1.a1', 'old_label': '27.d1', 'projective_image': '243.37', 'quotient_action_image': '9.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '27.d1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312290
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '27.e1', 'aut_quo_index': 8, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['9.c1', '9.n1', '9.o1'], 'contains': ['54.e1', '81.c1', '81.g1'], 'core': '27.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [7593, 1898, 4389, 739], 'generators': [729, 163, 549, 486], 'label': '1458.318.27.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '27.e1', 'normal_contained_in': ['9.c1'], 'normal_contains': ['54.e1', '81.c1'], 'normalizer': '1.a1', 'old_label': '27.e1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312291
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2187, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '9.f1'], 'contains': ['54.f1', '81.a1', '81.e1', '81.f1'], 'core': '81.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [711, -1, 4101, -1], 'generators': [729, 162, 999, 486], 'label': '1458.318.27.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.f1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312292
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '27.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.c1', '9.f1'], 'contains': ['54.g1', '81.a1', '81.g1'], 'core': '81.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5632, -1, 2025, -1], 'generators': [729, 163, 999, 486], 'label': '1458.318.27.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.g1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.g1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312293
    {'ambient': '1458.318', 'aut_centralizer_order': 9, 'aut_label': '3.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '81.a1', 'complements': ['486.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.c1', '9.b1', '9.d1', '9.j1', '9.l1'], 'core': '3.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2688, 9490, 5869, 7289], 'generators': [729, 486, 9, 3, 162, 999], 'label': '1458.318.3.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.c1', '9.b1', '9.d1'], 'normalizer': '1.a1', 'old_label': '3.c1', 'projective_image': '243.37', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.c1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312294
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '27.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '108.28', 'aut_weyl_index': 729, 'centralizer': '27.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.d1', '9.g1'], 'contains': ['54.h1', '81.a1', '81.h1'], 'core': '81.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6418, -1, 6887, -1], 'generators': [729, 3, 999, 486], 'label': '1458.318.27.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '27.h1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.h1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312295
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '27.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['9.e1', '9.g1'], 'contains': ['54.i1', '81.a1', '81.i1'], 'core': '81.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8089, -1, 8713, -1], 'generators': [729, 544, 999, 486], 'label': '1458.318.27.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '27.i1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.i1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312296
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '27.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.17', 'aut_weyl_index': 729, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.h1', '9.i1'], 'contains': ['54.j1', '81.b1', '81.d1', '81.k1'], 'core': '81.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2827, -1, 121, -1], 'generators': [729, 1, 9, 486], 'label': '1458.318.27.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.j1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.j1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312297
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '27.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.c1', '9.h1', '9.i1'], 'contains': ['54.k1', '81.b1', '81.g1'], 'core': '81.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3110, -1, 1737, -1], 'generators': [729, 163, 9, 486], 'label': '1458.318.27.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.k1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.k1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312298
    {'ambient': '1458.318', 'aut_centralizer_order': 162, 'aut_label': '27.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.d1', '9.j1', '9.l1'], 'contains': ['54.l1', '81.b1', '81.h1'], 'core': '81.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [132, -1, 6340, -1], 'generators': [729, 3, 9, 486], 'label': '1458.318.27.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '27.l1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.l1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312299
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '27.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['9.e1', '9.k1', '9.m1'], 'contains': ['54.m1', '81.b1', '81.i1'], 'core': '81.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9282, -1, 9295, -1], 'generators': [729, 544, 9, 486], 'label': '1458.318.27.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '27.m1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.m1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312300
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '27.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.a1', '9.n1'], 'contains': ['54.n1', '81.c1', '81.d1'], 'core': '81.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3493, -1, 3012, -1], 'generators': [729, 1, 1008, 486], 'label': '1458.318.27.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.n1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.n1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312301
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '27.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 4374, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.b1', '9.n1'], 'contains': ['54.o1', '81.c1', '81.e1', '81.f1'], 'core': '81.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [999, -1, 4677, -1], 'generators': [729, 162, 1008, 486], 'label': '1458.318.27.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.o1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.o1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312302
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '27.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.c1', '9.n1'], 'contains': ['54.p1', '81.c1', '81.g1'], 'core': '81.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [5993, -1, 3814, -1], 'generators': [729, 163, 1008, 486], 'label': '1458.318.27.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.p1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.p1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312303
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '27.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['9.d1', '9.o1'], 'contains': ['54.q1', '81.c1', '81.h1'], 'core': '81.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [8383, -1, 7466, -1], 'generators': [729, 3, 1008, 486], 'label': '1458.318.27.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '27.q1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.q1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312304
    {'ambient': '1458.318', 'aut_centralizer_order': 9, 'aut_label': '3.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '81.c1', 'complements': ['486.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['6.d1', '9.b1', '9.e1', '9.k1', '9.m1'], 'core': '3.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [6682, 8145, 8118, 8492], 'generators': [729, 486, 9, 544, 162, 999], 'label': '1458.318.3.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.d1', '9.b1', '9.e1'], 'normalizer': '1.a1', 'old_label': '3.d1', 'projective_image': '243.37', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.d1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 76312305
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '27.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['9.e1', '9.o1'], 'contains': ['54.r1', '81.c1', '81.i1'], 'core': '81.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [9868, -1, 9582, -1], 'generators': [729, 544, 549, 486], 'label': '1458.318.27.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '27.r1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.r1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312306
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '27.r2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['9.e1', '9.o1'], 'contains': ['54.r2', '81.c1', '81.i1'], 'core': '81.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [9577, -1, 9870, -1], 'generators': [729, 544, 1008, 486], 'label': '1458.318.27.r2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '27.r2', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.r2', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312307
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '27.s1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2187, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['9.f1', '9.h1', '9.n1'], 'contains': ['54.s1', '81.d1', '81.e1', '81.g1'], 'core': '243.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1583, -1, 1256, -1], 'generators': [729, 1, 162, 486], 'label': '1458.318.27.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.s1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.s1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312308
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '27.t1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '18.3', 'aut_weyl_index': 4374, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['9.f1', '9.i1', '9.n1'], 'contains': ['54.t1', '81.d1', '81.f1', '81.g1'], 'core': '243.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1291, -1, 968, -1], 'generators': [729, 1, 1161, 486], 'label': '1458.318.27.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.t1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.t1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312309
    {'ambient': '1458.318', 'aut_centralizer_order': 2187, 'aut_label': '54.a1', 'aut_quo_index': 936, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 2187, 'centralizer': '9.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.b1', '18.c1', '18.d1', '18.e1', '27.a1'], 'contains': ['162.a1', '162.b1', '162.c1', '162.j1'], 'core': '54.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6790, 4379, 5698, 4926], 'generators': [9, 999, 486], 'label': '1458.318.54.a1', 'mobius_quo': 0, 'mobius_sub': 27, 'normal_closure': '54.a1', 'normal_contained_in': ['18.a1', '18.b1', '18.c1', '18.d1', '18.e1', '27.a1'], 'normal_contains': ['162.a1', '162.b1', '162.c1'], 'normalizer': '1.a1', 'old_label': '54.a1', 'projective_image': '486.196', 'quotient_action_image': '9.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312310
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '54.b1', 'aut_quo_index': 8, 'aut_stab_index': 3, 'aut_weyl_group': '108.17', 'aut_weyl_index': 729, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['18.a1', '18.f1', '18.g1', '27.b1'], 'contains': ['162.a1', '162.d1'], 'core': '54.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4922, 3453, 3153, 3822], 'generators': [1, 999], 'label': '1458.318.54.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.b1', 'normal_contained_in': ['18.a1', '27.b1'], 'normal_contains': ['162.a1'], 'normalizer': '1.a1', 'old_label': '54.b1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312311
    {'ambient': '1458.318', 'aut_centralizer_order': 4374, 'aut_label': '54.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '18.3', 'aut_weyl_index': 4374, 'centralizer': '3.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.h1', '18.j1', '18.k1', '27.c1'], 'contains': ['162.b1', '162.e1'], 'core': '54.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4639, 6535, 5271, 7694], 'generators': [162, 9], 'label': '1458.318.54.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.c1', 'normal_contained_in': ['18.b1', '27.c1'], 'normal_contains': ['162.b1'], 'normalizer': '1.a1', 'old_label': '54.c1', 'projective_image': '486.196', 'quotient_action_image': '3.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312312
    {'ambient': '1458.318', 'aut_centralizer_order': 2187, 'aut_label': '54.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '18.3', 'aut_weyl_index': 4374, 'centralizer': '9.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '18.i1', '18.l1', '18.m1', '27.d1'], 'contains': ['162.b1', '162.f1'], 'core': '54.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3772, 5718, 4797, 6284], 'generators': [1161, 9], 'label': '1458.318.54.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.d1', 'normal_contained_in': ['18.b1', '27.d1'], 'normal_contains': ['162.b1'], 'normalizer': '1.a1', 'old_label': '54.d1', 'projective_image': '486.196', 'quotient_action_image': '9.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312313
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '54.e1', 'aut_quo_index': 8, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['18.c1', '18.n1', '18.o1', '27.e1'], 'contains': ['162.c1', '162.g1'], 'core': '54.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [7241, 1898, 4361, 2604], 'generators': [163, 549], 'label': '1458.318.54.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.e1', 'normal_contained_in': ['18.c1', '27.e1'], 'normal_contains': ['162.c1'], 'normalizer': '1.a1', 'old_label': '54.e1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312314
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2187, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.f1', '27.f1'], 'contains': ['162.a1', '162.e1', '162.f1'], 'core': '162.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2252, -1, 4009, -1], 'generators': [162, 999], 'label': '1458.318.54.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.f1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312315
    {'ambient': '1458.318', 'aut_centralizer_order': 3, 'aut_label': '3.e1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '243.a1', 'complements': ['486.e1'], 'conjugacy_class_count': 6, 'contained_in': ['1.a1'], 'contains': ['6.e1', '9.c1', '9.d1', '9.e1', '9.o1'], 'core': '3.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [7272, 4445, 7490, 3713], 'generators': [729, 486, 549, 163, 3, 999], 'label': '1458.318.3.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.e1', '9.c1', '9.d1', '9.e1'], 'normalizer': '1.a1', 'old_label': '3.e1', 'projective_image': '243.37', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.e1', 'subgroup_fusion': None, 'weyl_group': '243.37'}
  • id: 76312316
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '18.f1', '27.g1'], 'contains': ['162.a1', '162.g1'], 'core': '162.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5289, -1, 3010, -1], 'generators': [163, 999], 'label': '1458.318.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.g1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312317
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '108.28', 'aut_weyl_index': 729, 'centralizer': '27.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.d1', '18.g1', '27.h1'], 'contains': ['162.a1', '162.h1'], 'core': '162.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6396, -1, 6887, -1], 'generators': [3, 999], 'label': '1458.318.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.h1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312318
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.e1', '18.g1', '27.i1'], 'contains': ['162.a1', '162.i1'], 'core': '162.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7908, -1, 8078, -1], 'generators': [544, 999], 'label': '1458.318.54.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.i1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312319
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.17', 'aut_weyl_index': 729, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.h1', '18.i1', '27.j1'], 'contains': ['162.b1', '162.d1', '162.k1'], 'core': '162.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3965, -1, 1833, -1], 'generators': [1, 9, 486], 'label': '1458.318.54.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.j1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312320
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '18.h1', '18.i1', '27.k1'], 'contains': ['162.b1', '162.g1'], 'core': '162.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4236, -1, 2658, -1], 'generators': [163, 9], 'label': '1458.318.54.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.k1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312321
    {'ambient': '1458.318', 'aut_centralizer_order': 162, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.d1', '18.j1', '18.l1', '27.l1'], 'contains': ['162.b1', '162.h1'], 'core': '162.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4437, -1, 6389, -1], 'generators': [3, 9], 'label': '1458.318.54.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '54.l1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312322
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.e1', '18.k1', '18.m1', '27.m1'], 'contains': ['162.b1', '162.i1'], 'core': '162.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [8579, -1, 8238, -1], 'generators': [544, 9], 'label': '1458.318.54.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '54.m1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312323
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.n1', '27.n1'], 'contains': ['162.c1', '162.d1'], 'core': '162.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3522, -1, 3278, -1], 'generators': [1, 1008], 'label': '1458.318.54.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.n1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312324
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 4374, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '18.n1', '27.o1'], 'contains': ['162.c1', '162.e1', '162.f1'], 'core': '162.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [2800, -1, 4560, -1], 'generators': [162, 1008], 'label': '1458.318.54.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.o1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312325
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '18.n1', '27.p1'], 'contains': ['162.c1', '162.g1'], 'core': '162.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [5993, -1, 3522, -1], 'generators': [163, 1008], 'label': '1458.318.54.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.p1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312326
    {'ambient': '1458.318', 'aut_centralizer_order': 27, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 27, 'centralizer': '27.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['18.a1', '18.b1', '18.c1', '18.f1', '18.h1', '18.i1', '18.n1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3900, 510, 3008, 2309], 'generators': [1, 162, 9, 999], 'label': '1458.318.6.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1', '3.a1'], 'normal_contains': ['18.a1', '18.b1', '18.c1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312327
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.d1', '18.o1', '27.q1'], 'contains': ['162.c1', '162.h1'], 'core': '162.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [8383, -1, 7175, -1], 'generators': [3, 1008], 'label': '1458.318.54.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '54.q1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312328
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '27.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.e1', '18.o1', '27.r1'], 'contains': ['162.c1', '162.i1'], 'core': '162.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [8916, -1, 8437, -1], 'generators': [544, 549], 'label': '1458.318.54.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '54.r1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312329
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '54.r2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.8', 'aut_weyl_index': 1458, 'centralizer': '81.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.e1', '18.o1', '27.r2'], 'contains': ['162.c1', '162.i1'], 'core': '162.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [9117, -1, 8636, -1], 'generators': [544, 1008], 'label': '1458.318.54.r2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '54.r2', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r2', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 76312330
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2187, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['18.f1', '18.h1', '18.n1', '27.s1'], 'contains': ['162.d1', '162.e1', '162.g1'], 'core': '486.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2560, -1, 2421, -1], 'generators': [1, 162], 'label': '1458.318.54.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.s1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312331
    {'ambient': '1458.318', 'aut_centralizer_order': 81, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '18.3', 'aut_weyl_index': 4374, 'centralizer': '27.c1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['18.f1', '18.i1', '18.n1', '27.t1'], 'contains': ['162.d1', '162.f1', '162.g1'], 'core': '486.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2051, -1, 2222, -1], 'generators': [1, 1161], 'label': '1458.318.54.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.t1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 76312332
    {'ambient': '1458.318', 'aut_centralizer_order': 6561, 'aut_label': '81.a1', 'aut_quo_index': 72, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 6561, 'centralizer': '3.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.b1', '27.f1', '27.g1', '27.h1', '27.i1'], 'contains': ['162.a1', '243.a1', '243.b1'], 'core': '81.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5443, 4913, 5508, 4361], 'generators': [729, 999, 486], 'label': '1458.318.81.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '81.a1', 'normal_contained_in': ['27.a1', '27.b1'], 'normal_contains': ['162.a1', '243.a1'], 'normalizer': '1.a1', 'old_label': '81.a1', 'projective_image': '243.37', 'quotient_action_image': '3.1', 'quotient_action_kernel': '27.3', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312333
    {'ambient': '1458.318', 'aut_centralizer_order': 13122, 'aut_label': '81.b1', 'aut_quo_index': 216, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13122, 'centralizer': '3.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.c1', '27.d1', '27.j1', '27.k1', '27.l1', '27.m1'], 'contains': ['162.b1', '243.a1', '243.c1'], 'core': '81.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4106, 6463, 5034, 6989], 'generators': [729, 9, 486], 'label': '1458.318.81.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '81.b1', 'normal_contained_in': ['27.a1', '27.c1', '27.d1'], 'normal_contains': ['162.b1', '243.a1'], 'normalizer': '1.a1', 'old_label': '81.b1', 'projective_image': '243.37', 'quotient_action_image': '3.1', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312334
    {'ambient': '1458.318', 'aut_centralizer_order': 6561, 'aut_label': '81.c1', 'aut_quo_index': 144, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13122, 'centralizer': '3.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['27.a1', '27.e1', '27.n1', '27.o1', '27.p1', '27.q1', '27.r1', '27.r2'], 'contains': ['162.c1', '243.a1', '243.d1'], 'core': '81.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6623, 3412, 5888, 3283], 'generators': [729, 1008, 486], 'label': '1458.318.81.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '81.c1', 'normal_contained_in': ['27.a1', '27.e1'], 'normal_contains': ['162.c1', '243.a1'], 'normalizer': '1.a1', 'old_label': '81.c1', 'projective_image': '243.37', 'quotient_action_image': '3.1', 'quotient_action_kernel': '27.3', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '81.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312335
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '81.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 6561, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.b1', '27.j1', '27.n1', '27.s1', '27.t1'], 'contains': ['162.d1', '243.a1', '243.e1'], 'core': '243.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3156, -1, 2023, -1], 'generators': [729, 1, 486], 'label': '1458.318.81.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '81.d1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312336
    {'ambient': '1458.318', 'aut_centralizer_order': 4374, 'aut_label': '81.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.c1', '27.f1', '27.o1', '27.s1'], 'contains': ['162.e1', '243.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1533, -1, 4204, -1], 'generators': [729, 162, 486], 'label': '1458.318.81.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '81.e1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312337
    {'ambient': '1458.318', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '8748.nx', 'aut_weyl_index': 9, 'centralizer': '243.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '3.b1'], 'contains': ['18.a1', '18.d1', '18.e1', '18.g1'], 'core': '6.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6047, 3532, 7116, 6258], 'generators': [1, 3, 9], 'label': '1458.318.6.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1', 'normal_contained_in': ['2.a1', '3.b1'], 'normal_contains': ['18.a1', '18.d1', '18.e1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '243.37'}
  • id: 76312338
    {'ambient': '1458.318', 'aut_centralizer_order': 2187, 'aut_label': '81.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.d1', '27.f1', '27.o1', '27.t1'], 'contains': ['162.f1', '243.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1091, -1, 3814, -1], 'generators': [729, 1161, 486], 'label': '1458.318.81.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '81.f1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312339
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '81.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['27.e1', '27.g1', '27.k1', '27.p1', '27.s1', '27.t1'], 'contains': ['162.g1', '243.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4438, -1, 2853, -1], 'generators': [729, 163, 486], 'label': '1458.318.81.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '81.g1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312340
    {'ambient': '1458.318', 'aut_centralizer_order': 486, 'aut_label': '81.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '27.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.h1', '27.l1', '27.q1'], 'contains': ['162.h1', '243.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5976, -1, 6643, -1], 'generators': [729, 3, 486], 'label': '1458.318.81.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1', 'old_label': '81.h1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312341
    {'ambient': '1458.318', 'aut_centralizer_order': 243, 'aut_label': '81.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.2', 'aut_weyl_index': 13122, 'centralizer': '27.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['27.i1', '27.m1', '27.r1', '27.r2'], 'contains': ['162.i1', '243.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9173, -1, 9044, -1], 'generators': [729, 544, 486], 'label': '1458.318.81.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.e1', 'old_label': '81.i1', 'projective_image': '243.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.i1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312342
    {'ambient': '1458.318', 'aut_centralizer_order': 4374, 'aut_label': '81.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 39366, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1'], 'contains': ['162.j1', '243.b1', '243.c1', '243.d1'], 'core': '729.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6241, -1, 6125, -1], 'generators': [729, 495, 999], 'label': '1458.318.81.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '81.j1', 'projective_image': '729.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312343
    {'ambient': '1458.318', 'aut_centralizer_order': 486, 'aut_label': '81.k1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13122, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.j1'], 'contains': ['162.k1', '243.c1', '243.e1'], 'core': '729.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3665, -1, 1643, -1], 'generators': [729, 1, 495], 'label': '1458.318.81.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.h1', 'old_label': '81.k1', 'projective_image': '729.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 76312344
    {'ambient': '1458.318', 'aut_centralizer_order': 6561, 'aut_label': '162.a1', 'aut_quo_index': 72, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 6561, 'centralizer': '3.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.b1', '54.f1', '54.g1', '54.h1', '54.i1', '81.a1'], 'contains': ['486.a1', '486.b1'], 'core': '162.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5289, 4475, 5302, 4159], 'generators': [999, 486], 'label': '1458.318.162.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '162.a1', 'normal_contained_in': ['54.a1', '54.b1', '81.a1'], 'normal_contains': ['486.a1'], 'normalizer': '1.a1', 'old_label': '162.a1', 'projective_image': '486.196', 'quotient_action_image': '3.1', 'quotient_action_kernel': '54.10', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312345
    {'ambient': '1458.318', 'aut_centralizer_order': 13122, 'aut_label': '162.b1', 'aut_quo_index': 216, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13122, 'centralizer': '3.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.c1', '54.d1', '54.j1', '54.k1', '54.l1', '54.m1', '81.b1'], 'contains': ['486.a1', '486.c1'], 'core': '162.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4888, 5712, 5034, 6284], 'generators': [9, 486], 'label': '1458.318.162.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '162.b1', 'normal_contained_in': ['54.a1', '54.c1', '54.d1', '81.b1'], 'normal_contains': ['486.a1'], 'normalizer': '1.a1', 'old_label': '162.b1', 'projective_image': '486.196', 'quotient_action_image': '3.1', 'quotient_action_kernel': '54.15', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312346
    {'ambient': '1458.318', 'aut_centralizer_order': 6561, 'aut_label': '162.c1', 'aut_quo_index': 144, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 13122, 'centralizer': '3.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '54.e1', '54.n1', '54.o1', '54.p1', '54.q1', '54.r1', '54.r2', '81.c1'], 'contains': ['486.a1', '486.d1'], 'core': '162.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6623, 3441, 5445, 3610], 'generators': [1008, 486], 'label': '1458.318.162.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '162.c1', 'normal_contained_in': ['54.a1', '54.e1', '81.c1'], 'normal_contains': ['486.a1'], 'normalizer': '1.a1', 'old_label': '162.c1', 'projective_image': '486.196', 'quotient_action_image': '3.1', 'quotient_action_kernel': '54.10', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 76312347
    {'ambient': '1458.318', 'aut_centralizer_order': 729, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 6561, 'centralizer': '9.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['54.b1', '54.j1', '54.n1', '54.s1', '54.t1', '81.d1'], 'contains': ['486.a1', '486.e1'], 'core': '486.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3343, -1, 2340, -1], 'generators': [1, 486], 'label': '1458.318.162.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '162.d1', 'projective_image': '486.196', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}