Abstract group data - 1944.2732

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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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [18, 18, 4, 12], 'aut_gens': [[1, 2, 12, 108], [1397, 1718, 732, 144], [1637, 850, 1320, 1440], [439, 1142, 216, 1020], [1735, 1166, 1728, 996]], 'aut_group': None, 'aut_hash': 4441761044895498153, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 69984, 'aut_permdeg': 108, 'aut_perms': [642413570516186756901777598869956672829784281318437253878694932599206768177750970562576221556531853578567649856865583248113096938918298776476732832635789982505812181019398931, 935751858325545015179786626404902735494641804993322458525707755107324859123851178568737780648896753487017413417639580108161731527463033372424966792415300479333334824993722756, 83589666543244240574969540436419249634498922531327172835558403147509852522965823237249981852980950373229359912094891458572377157065645733305903445728478911814611583942554397, 547634117846508681313213477117458671725634830462715578549227297085434390974251377222198618030190873383106842740821285471651135431416067938845240992653574032758837804286934580], 'aut_phi_ratio': 108.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 27, 4, 1], [2, 81, 2, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 18, 1, 1], [6, 2, 2, 1], [6, 4, 1, 1], [6, 18, 1, 1], [6, 54, 4, 1], [6, 162, 2, 1], [9, 6, 6, 1], [9, 12, 3, 1], [9, 36, 2, 2], [18, 6, 6, 1], [18, 12, 3, 1], [18, 36, 2, 2], [18, 54, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_9^2.C_6^2.C_6.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '17496.rx', 'autcentquo_hash': 1152853215005446682, 'autcentquo_nilpotent': False, 'autcentquo_order': 17496, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^5.\\SOPlus(4,2)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 27, 4], [2, 81, 2], [3, 2, 2], [3, 4, 1], [3, 18, 1], [6, 2, 2], [6, 4, 1], [6, 18, 1], [6, 54, 4], [6, 162, 2], [9, 6, 6], [9, 12, 3], [9, 36, 4], [18, 6, 6], [18, 12, 3], [18, 36, 4], [18, 54, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '972.477', 'commutator_count': 1, 'commutator_label': '243.45', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2732, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['972.477', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 27, 1, 4], [2, 81, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [3, 18, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 18, 1, 1], [6, 54, 1, 4], [6, 162, 1, 2], [9, 6, 3, 2], [9, 12, 3, 1], [9, 36, 1, 2], [9, 36, 2, 1], [18, 6, 3, 2], [18, 12, 3, 1], [18, 36, 1, 2], [18, 36, 2, 1], [18, 54, 3, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24192, 'exponent': 18, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 3]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '216.172', 'hash': 2732, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [2, 6, 9, 9], 'inner_gens': [[1, 10, 96, 108], [5, 2, 1392, 1908], [25, 674, 12, 108], [1, 254, 12, 108]], 'inner_hash': 477, 'inner_nilpotent': False, 'inner_order': 972, 'inner_split': True, 'inner_tex': 'C_9^2:D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 12, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 12], [4, 10], [6, 24], [12, 6]], 'label': '1944.2732', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*C9^2:D6', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 60, 'number_divisions': 38, 'number_normal_subgroups': 45, 'number_subgroup_autclasses': 136, 'number_subgroup_classes': 317, 'number_subgroups': 6260, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 271], [3, 26], [6, 566], [9, 216], [18, 864]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 2, 6], 'outer_gen_pows': [0, 6, 0], 'outer_gens': [[973, 10, 60, 756], [7, 2, 432, 996], [973, 982, 96, 756]], 'outer_group': '72.30', 'outer_hash': 30, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 10, 'outer_perms': [458663, 1629362, 448576], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\wr C_2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 56, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 6], [8, 2], [18, 8], [36, 2]], 'representations': {'PC': {'code': 3391976350479193807980763946835140520388550996753926005197367867, 'gens': [1, 2, 4, 6], 'pres': [8, 2, 2, 3, 3, 3, 2, 3, 3, 161, 41, 194, 3075, 22283, 10483, 123, 2884, 1452, 45805, 2181, 141, 49406, 3550, 222, 41487]}, 'Perm': {'d': 56, 'gens': [696886881073030102998137654606121540472624633203928879308426832978789052, 21942405696302040634834949752021455683790469606837340730665712936313339, 304888344611713860501504000000, 927741467886879589089117228885538833407782259204702457300470902047011756, 13406276201022569384351897994737487986071446017428753252076937765171294261, 26573171162550518142122935482810006605676460448616308980074836404069419733, 1307474914906274299363669138, 39043087879893948645473269616772563227596882428860796150746730987520000000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_9^2:D_6', 'transitive_degree': 108, '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: 136824090
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 2732, 'group_order': 1944, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 136824101
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 2732, 'group_order': 1944, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 972, 'size': 1}
  • id: 136824112
    {'aut_label': '2B', 'centralizer': '27.b1', 'counter': 3, 'group_counter': 2732, 'group_order': 1944, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 331, 'size': 27}
  • id: 136824123
    {'aut_label': '2B', 'centralizer': '27.b1', 'counter': 4, 'group_counter': 2732, 'group_order': 1944, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 973, 'size': 27}
  • id: 136824134
    {'aut_label': '2B', 'centralizer': '27.b1', 'counter': 5, 'group_counter': 2732, 'group_order': 1944, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1519, 'size': 27}
  • id: 136824145
    {'aut_label': '2B', 'centralizer': '27.b1', 'counter': 6, 'group_counter': 2732, 'group_order': 1944, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 753, 'size': 27}
  • id: 136824147
    {'aut_label': '2F', 'centralizer': '81.b1', 'counter': 7, 'group_counter': 2732, 'group_order': 1944, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 54, 'size': 81}
  • id: 136824148
    {'aut_label': '2F', 'centralizer': '81.b1', 'counter': 8, 'group_counter': 2732, 'group_order': 1944, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 594, 'size': 81}
  • id: 136824149
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 2732, 'group_order': 1944, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 648, 'size': 2}
  • id: 136824091
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 2732, 'group_order': 1944, 'label': '3B', 'order': 3, 'powers': [10, 1], 'representative': 72, 'size': 2}
  • id: 136824092
    {'aut_label': '3C', 'centralizer': '4.a1', 'counter': 11, 'group_counter': 2732, 'group_order': 1944, 'label': '3C', 'order': 3, 'powers': [11, 1], 'representative': 720, 'size': 4}
  • id: 136824093
    {'aut_label': '3D', 'centralizer': '18.e1', 'counter': 12, 'group_counter': 2732, 'group_order': 1944, 'label': '3D', 'order': 3, 'powers': [12, 1], 'representative': 656, 'size': 18}
  • id: 136824094
    {'aut_label': '6A', 'centralizer': '2.a1', 'counter': 13, 'group_counter': 2732, 'group_order': 1944, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 324, 'size': 2}
  • id: 136824095
    {'aut_label': '6A', 'centralizer': '2.a1', 'counter': 14, 'group_counter': 2732, 'group_order': 1944, 'label': '6B', 'order': 6, 'powers': [10, 2], 'representative': 1008, 'size': 2}
  • id: 136824096
    {'aut_label': '6C', 'centralizer': '4.a1', 'counter': 15, 'group_counter': 2732, 'group_order': 1944, 'label': '6C', 'order': 6, 'powers': [11, 2], 'representative': 360, 'size': 4}
  • id: 136824097
    {'aut_label': '6D', 'centralizer': '18.e1', 'counter': 16, 'group_counter': 2732, 'group_order': 1944, 'label': '6D', 'order': 6, 'powers': [12, 2], 'representative': 328, 'size': 18}
  • id: 136824098
    {'aut_label': '6E', 'centralizer': '54.a1', 'counter': 17, 'group_counter': 2732, 'group_order': 1944, 'label': '6E', 'order': 6, 'powers': [10, 3], 'representative': 367, 'size': 54}
  • id: 136824099
    {'aut_label': '6E', 'centralizer': '54.a1', 'counter': 18, 'group_counter': 2732, 'group_order': 1944, 'label': '6F', 'order': 6, 'powers': [9, 4], 'representative': 1621, 'size': 54}
  • id: 136824100
    {'aut_label': '6E', 'centralizer': '54.a1', 'counter': 19, 'group_counter': 2732, 'group_order': 1944, 'label': '6G', 'order': 6, 'powers': [10, 5], 'representative': 1591, 'size': 54}
  • id: 136824102
    {'aut_label': '6E', 'centralizer': '54.a1', 'counter': 20, 'group_counter': 2732, 'group_order': 1944, 'label': '6H', 'order': 6, 'powers': [9, 6], 'representative': 105, 'size': 54}
  • id: 136824103
    {'aut_label': '6I', 'centralizer': '162.d1', 'counter': 21, 'group_counter': 2732, 'group_order': 1944, 'label': '6I', 'order': 6, 'powers': [12, 7], 'representative': 706, 'size': 162}
  • id: 136824104
    {'aut_label': '6I', 'centralizer': '162.d1', 'counter': 22, 'group_counter': 2732, 'group_order': 1944, 'label': '6J', 'order': 6, 'powers': [12, 8], 'representative': 1922, 'size': 162}
  • id: 136824105
    {'aut_label': '9A1', 'centralizer': '6.e1', 'counter': 23, 'group_counter': 2732, 'group_order': 1944, 'label': '9A1', 'order': 9, 'powers': [24, 9], 'representative': 216, 'size': 6}
  • id: 136824106
    {'aut_label': '9A1', 'centralizer': '6.e1', 'counter': 24, 'group_counter': 2732, 'group_order': 1944, 'label': '9A2', 'order': 9, 'powers': [25, 9], 'representative': 432, 'size': 6}
  • id: 136824107
    {'aut_label': '9A1', 'centralizer': '6.e1', 'counter': 25, 'group_counter': 2732, 'group_order': 1944, 'label': '9A4', 'order': 9, 'powers': [23, 9], 'representative': 864, 'size': 6}
  • id: 136824108
    {'aut_label': '9A1', 'centralizer': '6.e1', 'counter': 26, 'group_counter': 2732, 'group_order': 1944, 'label': '9B1', 'order': 9, 'powers': [27, 10], 'representative': 672, 'size': 6}
  • id: 136824109
    {'aut_label': '9A1', 'centralizer': '6.e1', 'counter': 27, 'group_counter': 2732, 'group_order': 1944, 'label': '9B2', 'order': 9, 'powers': [28, 10], 'representative': 1344, 'size': 6}
  • id: 136824110
    {'aut_label': '9A1', 'centralizer': '6.e1', 'counter': 28, 'group_counter': 2732, 'group_order': 1944, 'label': '9B4', 'order': 9, 'powers': [26, 10], 'representative': 744, 'size': 6}
  • id: 136824111
    {'aut_label': '9C1', 'centralizer': '12.b1', 'counter': 29, 'group_counter': 2732, 'group_order': 1944, 'label': '9C1', 'order': 9, 'powers': [30, 11], 'representative': 240, 'size': 12}
  • id: 136824113
    {'aut_label': '9C1', 'centralizer': '12.b1', 'counter': 30, 'group_counter': 2732, 'group_order': 1944, 'label': '9C2', 'order': 9, 'powers': [31, 11], 'representative': 480, 'size': 12}
  • id: 136824114
    {'aut_label': '9C1', 'centralizer': '12.b1', 'counter': 31, 'group_counter': 2732, 'group_order': 1944, 'label': '9C4', 'order': 9, 'powers': [29, 11], 'representative': 960, 'size': 12}
  • id: 136824115
    {'aut_label': '9D', 'centralizer': '36.d1', 'counter': 32, 'group_counter': 2732, 'group_order': 1944, 'label': '9D', 'order': 9, 'powers': [32, 9], 'representative': 296, 'size': 36}
  • id: 136824116
    {'aut_label': '9D', 'centralizer': '36.d1', 'counter': 33, 'group_counter': 2732, 'group_order': 1944, 'label': '9E', 'order': 9, 'powers': [33, 10], 'representative': 32, 'size': 36}
  • id: 136824117
    {'aut_label': '9F1', 'centralizer': '36.e1', 'counter': 34, 'group_counter': 2732, 'group_order': 1944, 'label': '9F1', 'order': 9, 'powers': [35, 11], 'representative': 1616, 'size': 36}
  • id: 136824118
    {'aut_label': '9F1', 'centralizer': '36.e1', 'counter': 35, 'group_counter': 2732, 'group_order': 1944, 'label': '9F-1', 'order': 9, 'powers': [34, 11], 'representative': 1816, 'size': 36}
  • id: 136824119
    {'aut_label': '18A1', 'centralizer': '6.e1', 'counter': 36, 'group_counter': 2732, 'group_order': 1944, 'label': '18A1', 'order': 18, 'powers': [23, 13], 'representative': 108, 'size': 6}
  • id: 136824120
    {'aut_label': '18A1', 'centralizer': '6.e1', 'counter': 37, 'group_counter': 2732, 'group_order': 1944, 'label': '18A5', 'order': 18, 'powers': [25, 13], 'representative': 1404, 'size': 6}
  • id: 136824121
    {'aut_label': '18A1', 'centralizer': '6.e1', 'counter': 38, 'group_counter': 2732, 'group_order': 1944, 'label': '18A7', 'order': 18, 'powers': [24, 13], 'representative': 756, 'size': 6}
  • id: 136824122
    {'aut_label': '18A1', 'centralizer': '6.e1', 'counter': 39, 'group_counter': 2732, 'group_order': 1944, 'label': '18B1', 'order': 18, 'powers': [26, 14], 'representative': 336, 'size': 6}
  • id: 136824124
    {'aut_label': '18A1', 'centralizer': '6.e1', 'counter': 40, 'group_counter': 2732, 'group_order': 1944, 'label': '18B5', 'order': 18, 'powers': [28, 14], 'representative': 372, 'size': 6}
  • id: 136824125
    {'aut_label': '18A1', 'centralizer': '6.e1', 'counter': 41, 'group_counter': 2732, 'group_order': 1944, 'label': '18B7', 'order': 18, 'powers': [27, 14], 'representative': 348, 'size': 6}
  • id: 136824126
    {'aut_label': '18C1', 'centralizer': '12.b1', 'counter': 42, 'group_counter': 2732, 'group_order': 1944, 'label': '18C1', 'order': 18, 'powers': [29, 15], 'representative': 120, 'size': 12}
  • id: 136824127
    {'aut_label': '18C1', 'centralizer': '12.b1', 'counter': 43, 'group_counter': 2732, 'group_order': 1944, 'label': '18C5', 'order': 18, 'powers': [31, 15], 'representative': 132, 'size': 12}
  • id: 136824128
    {'aut_label': '18C1', 'centralizer': '12.b1', 'counter': 44, 'group_counter': 2732, 'group_order': 1944, 'label': '18C7', 'order': 18, 'powers': [30, 15], 'representative': 156, 'size': 12}
  • id: 136824129
    {'aut_label': '18D', 'centralizer': '36.d1', 'counter': 45, 'group_counter': 2732, 'group_order': 1944, 'label': '18D', 'order': 18, 'powers': [32, 13], 'representative': 112, 'size': 36}
  • id: 136824130
    {'aut_label': '18D', 'centralizer': '36.d1', 'counter': 46, 'group_counter': 2732, 'group_order': 1944, 'label': '18E', 'order': 18, 'powers': [33, 14], 'representative': 340, 'size': 36}
  • id: 136824131
    {'aut_label': '18F1', 'centralizer': '36.e1', 'counter': 47, 'group_counter': 2732, 'group_order': 1944, 'label': '18F1', 'order': 18, 'powers': [34, 15], 'representative': 124, 'size': 36}
  • id: 136824132
    {'aut_label': '18F1', 'centralizer': '36.e1', 'counter': 48, 'group_counter': 2732, 'group_order': 1944, 'label': '18F-1', 'order': 18, 'powers': [35, 15], 'representative': 136, 'size': 36}
  • id: 136824133
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 49, 'group_counter': 2732, 'group_order': 1944, 'label': '18G1', 'order': 18, 'powers': [27, 17], 'representative': 415, 'size': 54}
  • id: 136824135
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 50, 'group_counter': 2732, 'group_order': 1944, 'label': '18G5', 'order': 18, 'powers': [26, 17], 'representative': 427, 'size': 54}
  • id: 136824136
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 51, 'group_counter': 2732, 'group_order': 1944, 'label': '18G7', 'order': 18, 'powers': [28, 17], 'representative': 379, 'size': 54}
  • id: 136824137
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 52, 'group_counter': 2732, 'group_order': 1944, 'label': '18H1', 'order': 18, 'powers': [25, 18], 'representative': 541, 'size': 54}
  • id: 136824138
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 53, 'group_counter': 2732, 'group_order': 1944, 'label': '18H5', 'order': 18, 'powers': [24, 18], 'representative': 757, 'size': 54}
  • id: 136824139
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 54, 'group_counter': 2732, 'group_order': 1944, 'label': '18H7', 'order': 18, 'powers': [23, 18], 'representative': 1837, 'size': 54}
  • id: 136824140
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 55, 'group_counter': 2732, 'group_order': 1944, 'label': '18I1', 'order': 18, 'powers': [27, 19], 'representative': 1543, 'size': 54}
  • id: 136824141
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 56, 'group_counter': 2732, 'group_order': 1944, 'label': '18I5', 'order': 18, 'powers': [26, 19], 'representative': 1531, 'size': 54}
  • id: 136824142
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 57, 'group_counter': 2732, 'group_order': 1944, 'label': '18I7', 'order': 18, 'powers': [28, 19], 'representative': 1579, 'size': 54}
  • id: 136824143
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 58, 'group_counter': 2732, 'group_order': 1944, 'label': '18J1', 'order': 18, 'powers': [24, 20], 'representative': 501, 'size': 54}
  • id: 136824144
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 59, 'group_counter': 2732, 'group_order': 1944, 'label': '18J5', 'order': 18, 'powers': [23, 20], 'representative': 1545, 'size': 54}
  • id: 136824146
    {'aut_label': '18G1', 'centralizer': '54.a1', 'counter': 60, 'group_counter': 2732, 'group_order': 1944, 'label': '18J7', 'order': 18, 'powers': [25, 20], 'representative': 1149, 'size': 54}
• 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: 12047316
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.1a', '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], 'schur_index': 1}
  • id: 12047327
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.1b', '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], 'schur_index': 1}
  • id: 12047338
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12047348
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12047349
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.1e', '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], 'schur_index': 1}
  • id: 12047350
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.1f', '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], 'schur_index': 1}
  • id: 12047351
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.1g', '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], 'schur_index': 1}
  • id: 12047352
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.1h', '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], 'schur_index': 1}
  • id: 12047353
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, -1, 2, 2, 2, -1, 0, 0, 0, 0, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047317
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, -1, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, -1, -1, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12047318
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047319
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, 2, 0, -2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, -1, -1, 1, 1, -1, 0, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047320
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, -2, 2, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, -2, 0, 2, 0, 0, 0, -1, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12047321
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 0, 0, -2, 2, 2, 2, 2, -1, -2, -2, -2, 1, 0, 0, 0, 0, 1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047322
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 0, 0, 2, -2, 2, 2, 2, -1, -2, -2, -2, 1, 0, 0, 0, 0, -1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047323
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, -2, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, 0, -2, 0, 0, 0, -1, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, -1, 1, 0, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12047324
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, -2, 0, 2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -1, -1, 1, 0, 0, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047325
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, -2, 0, -2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047326
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, -2, 0, 0, 0, -1, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12047328
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -1, 2, 2, 2, -1, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047329
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, 4, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, -2, 4, 4, 4, -2, -2, -2, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047330
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 4, -2, 4, -2, -2, 4, -2, -2, -2, 1, -2, 1, 1, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047331
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, 1, 1, -2, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047332
    {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.4d', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -4, -4, -4, 2, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, 4, -2, -2, -2, -2, -2, 1, 1, 1, 2, 2, 2, -4, -4, -4, 2, 2, 2, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047333
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.4e', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -4, -4, -4, 2, 0, 0, 0, 0, 0, 0, 4, -2, 4, -2, -2, 4, -2, -2, -2, 1, -2, 1, 1, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047334
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.4f', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, 1, 1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047335
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.4g', 'multiplicity': 2, 'nt': [12, 71], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 8, -4, 8, 8, 8, -4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, -1, -1, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047336
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.4h', 'multiplicity': 2, 'nt': [24, 548], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 8, 8, 8, -4, -8, -8, -8, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, -1, -1, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047337
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.6a', 'multiplicity': 3, 'nt': [27, 122], 'qdim': 18, 'qvalues': [18, 18, 0, 0, 6, 6, 0, 0, -9, 18, -9, 0, -9, 18, -9, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047339
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.6b', 'multiplicity': 3, 'nt': [27, 122], 'qdim': 18, 'qvalues': [18, 18, 6, 6, 0, 0, 0, 0, 18, -9, -9, 0, 18, -9, -9, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047340
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.6c', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -18, -6, 6, 0, 0, 0, 0, 18, -9, -9, 0, -18, 9, 9, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047341
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.6d', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -18, 0, 0, -6, 6, 0, 0, -9, 18, -9, 0, 9, -18, 9, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047342
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.6e', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -18, 0, 0, 6, -6, 0, 0, -9, 18, -9, 0, 9, -18, 9, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047343
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.6f', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -18, 6, -6, 0, 0, 0, 0, 18, -9, -9, 0, -18, 9, 9, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047344
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.6g', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, -6, -6, 0, 0, 0, 0, 18, -9, -9, 0, 18, -9, -9, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047345
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.6h', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, 0, 0, -6, -6, 0, 0, -9, 18, -9, 0, -9, 18, -9, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047346
    {'cdim': 12, 'counter': 37, 'faithful': False, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.12a', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 36, 'qvalues': [36, 36, 0, 0, 0, 0, 0, 0, -18, -18, 9, 0, -18, -18, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12047347
    {'cdim': 12, 'counter': 38, 'faithful': True, 'group': '1944.2732', 'group_order': 1944, 'image': None, 'label': '1944.2732.12b', 'multiplicity': 3, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -36, 0, 0, 0, 0, 0, 0, -18, -18, 9, 0, 18, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 27551851
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1944, 'label': '1944.2732.1a', '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]]]}
  • id: 27551862
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 972, 'label': '1944.2732.1b', '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]]]}
  • id: 27551873
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 972, 'label': '1944.2732.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 27551884
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 972, 'label': '1944.2732.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 27551895
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 972, 'label': '1944.2732.1e', '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]]]}
  • id: 27551906
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 972, 'label': '1944.2732.1f', '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]]]}
  • id: 27551908
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 972, 'label': '1944.2732.1g', '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]]]}
  • id: 27551909
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 972, 'label': '1944.2732.1h', '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]]]}
  • id: 27551910
    {'center': '6.b1', 'center_index': 6, 'center_order': 324, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1', 'kernel_order': 324, 'label': '1944.2732.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551852
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 324, 'label': '1944.2732.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 27551853
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 324, 'label': '1944.2732.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551854
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 162, 'label': '1944.2732.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551855
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 162, 'label': '1944.2732.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 27551856
    {'center': '6.b1', 'center_index': 6, 'center_order': 324, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1', 'kernel_order': 162, 'label': '1944.2732.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551857
    {'center': '6.b1', 'center_index': 6, 'center_order': 324, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1', 'kernel_order': 162, 'label': '1944.2732.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551858
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 162, 'label': '1944.2732.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 27551859
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 162, 'label': '1944.2732.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551860
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 162, 'label': '1944.2732.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551861
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 162, 'label': '1944.2732.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 27551863
    {'center': '6.b1', 'center_index': 6, 'center_order': 324, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 162, 'label': '1944.2732.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551864
    {'center': '36.b1', 'center_index': 36, 'center_order': 54, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1', 'kernel_order': 54, 'label': '1944.2732.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551865
    {'center': '36.b1', 'center_index': 36, 'center_order': 54, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1', 'kernel_order': 54, 'label': '1944.2732.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551866
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 54, 'label': '1944.2732.4c', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551867
    {'center': '36.b1', 'center_index': 36, 'center_order': 54, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.2732.4d', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551868
    {'center': '36.b1', 'center_index': 36, 'center_order': 54, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 27, 'label': '1944.2732.4e', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551869
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.2732.4f', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551870
    {'center': '108.a1', 'center_index': 108, 'center_order': 18, 'counter': 27, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '108.40', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1', 'kernel_order': 18, 'label': '1944.2732.4g1', 'nt': [12, 71], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551871
    {'center': '108.a1', 'center_index': 108, 'center_order': 18, 'counter': 28, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '108.40', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1', 'kernel_order': 18, 'label': '1944.2732.4g2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551872
    {'center': '108.a1', 'center_index': 108, 'center_order': 18, 'counter': 29, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '216.172', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.2732.4h1', 'nt': [24, 548], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551874
    {'center': '108.a1', 'center_index': 108, 'center_order': 18, 'counter': 30, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '216.172', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.2732.4h2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551875
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 31, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6a1', 'nt': [27, 122], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[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]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 27551876
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 32, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6a2', 'nt': [27, 122], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 4], [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]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 27551877
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 33, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6a3', 'nt': [27, 122], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]]]}
  • id: 27551878
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 34, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6b1', 'nt': [27, 122], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[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, -2]], [[3, 1], [3, -1]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551879
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 35, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6b2', 'nt': [27, 122], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[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]], [[3, 1], [3, -1]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551880
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 36, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6b3', 'nt': [27, 122], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551881
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 37, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6c1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[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, -2]], [[-3, 1], [-3, -1]], [[-3, 4], [-3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551882
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 38, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6c2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[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]], [[-3, 1], [-3, -1]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551883
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 39, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6c3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551885
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 40, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6d1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[-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]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 27551886
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 41, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6d2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 4], [-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]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 27551887
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 42, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6d3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]]]}
  • id: 27551888
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 43, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6e1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[-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]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]]]}
  • id: 27551889
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 44, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6e2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 4], [-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]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 27551890
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 45, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6e3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]]]}
  • id: 27551891
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 46, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6f1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[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, -2]], [[-3, 1], [-3, -1]], [[-3, 4], [-3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551892
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 47, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6f2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[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]], [[-3, 1], [-3, -1]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551893
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 48, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '648.611', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 3, 'label': '1944.2732.6f3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551894
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 49, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6g1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[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, -2]], [[3, 1], [3, -1]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551896
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 50, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6g2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[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]], [[3, 1], [3, -1]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551897
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 51, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6g3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551898
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 52, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6h1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[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]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 27551899
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 53, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6h2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 4], [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]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 27551900
    {'center': '324.a1', 'center_index': 324, 'center_order': 6, 'counter': 54, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '324.125', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1', 'kernel_order': 6, 'label': '1944.2732.6h3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]]]}
  • id: 27551901
    {'center': '972.a1', 'center_index': 972, 'center_order': 2, 'counter': 55, 'cyclotomic_n': 9, 'dim': 12, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '972.477', 'image_order': 972, 'indicator': 1, 'kernel': '972.a1', 'kernel_order': 2, 'label': '1944.2732.12a1', 'nt': [54, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[3, 4], [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]]]}
  • id: 27551902
    {'center': '972.a1', 'center_index': 972, 'center_order': 2, 'counter': 56, 'cyclotomic_n': 9, 'dim': 12, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '972.477', 'image_order': 972, 'indicator': 1, 'kernel': '972.a1', 'kernel_order': 2, 'label': '1944.2732.12a2', 'nt': [54, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[3, 1], [3, -1]], [[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, 4], [3, -4]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551903
    {'center': '972.a1', 'center_index': 972, 'center_order': 2, 'counter': 57, 'cyclotomic_n': 9, 'dim': 12, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '972.477', 'image_order': 972, 'indicator': 1, 'kernel': '972.a1', 'kernel_order': 2, 'label': '1944.2732.12a3', 'nt': [54, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[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]]]}
  • id: 27551904
    {'center': '972.a1', 'center_index': 972, 'center_order': 2, 'counter': 58, 'cyclotomic_n': 9, 'dim': 12, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.2732', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 1, 'label': '1944.2732.12b1', 'nt': [108, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[-3, 1], [-3, -1]], [[-3, 4], [-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]]]}
  • id: 27551905
    {'center': '972.a1', 'center_index': 972, 'center_order': 2, 'counter': 59, 'cyclotomic_n': 9, 'dim': 12, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.2732', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 1, 'label': '1944.2732.12b2', 'nt': [108, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[3, 1], [3, -1]], [[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, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27551907
    {'center': '972.a1', 'center_index': 972, 'center_order': 2, 'counter': 60, 'cyclotomic_n': 9, 'dim': 12, 'faithful': True, 'field': [-1, -3, 0, 1], 'group': '1944.2732', 'group_counter': 2732, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.2732', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 1, 'label': '1944.2732.12b3', 'nt': [108, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[-3, 2], [-3, -2]], [[-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]]]}
• 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: 107496511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1944, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1944.2732.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2732', 'subgroup_hash': 2732, 'subgroup_order': 1944, 'subgroup_tex': 'C_2\\times C_9^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 972, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.657', 'subgroup_hash': 657, 'subgroup_order': 972, 'subgroup_tex': 'C_9^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 972, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.658', 'subgroup_hash': 658, 'subgroup_order': 972, 'subgroup_tex': 'C_2\\times C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 972, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1944.2732.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', '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': '972.477', 'subgroup_hash': 477, 'subgroup_order': 972, 'subgroup_tex': 'C_9^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', '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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.296', 'subgroup_hash': 296, 'subgroup_order': 648, 'subgroup_tex': 'D_9\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.297', 'subgroup_hash': 297, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 486, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.204', 'subgroup_hash': 204, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 486, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.156', 'subgroup_hash': 156, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 486, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.157', 'subgroup_hash': 157, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 324, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.75', 'subgroup_hash': 75, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.74', 'subgroup_hash': 74, 'subgroup_order': 324, 'subgroup_tex': 'C_9:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.62', 'subgroup_hash': 62, 'subgroup_order': 324, 'subgroup_tex': 'C_2\\times C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.64', 'subgroup_hash': 64, 'subgroup_order': 324, 'subgroup_tex': 'C_{18}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.61', 'subgroup_hash': 61, 'subgroup_order': 324, 'subgroup_tex': 'C_9\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.63', 'subgroup_hash': 63, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.63', 'subgroup_hash': 63, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.36', 'subgroup_hash': 36, 'subgroup_order': 324, 'subgroup_tex': 'D_9^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.37', 'subgroup_hash': 37, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 243, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1944.2732.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.45', 'subgroup_hash': 45, 'subgroup_order': 243, 'subgroup_tex': 'C_9^2:C_3', 'supersolvable': True, 'sylow': 3}
  • id: 107496560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', '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': '216.101', 'subgroup_hash': 101, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.24', 'subgroup_hash': 24, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 162, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.23', 'subgroup_hash': 23, 'subgroup_order': 162, 'subgroup_tex': 'C_9\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.17', 'subgroup_hash': 17, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.16', 'subgroup_hash': 16, 'subgroup_order': 162, 'subgroup_tex': 'C_9:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.24', 'subgroup_hash': 24, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.25', 'subgroup_hash': 25, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.25', 'subgroup_hash': 25, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.4', 'subgroup_hash': 4, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.6', 'subgroup_hash': 6, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.3', 'subgroup_hash': 3, 'subgroup_order': 162, 'subgroup_tex': 'C_9\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', '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': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496586
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 81, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.2', 'subgroup_hash': 2, 'subgroup_order': 81, 'subgroup_tex': 'C_9^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.4', 'subgroup_hash': 4, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.4', 'subgroup_hash': 4, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', '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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.17', 'subgroup_hash': 17, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496594
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 54, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 54, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496597
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496605
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1', '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': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 27, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], '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: 107496623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 27, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], '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: 107496624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496628
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1', '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 18, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.40', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['S'], '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: 107496631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496632
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496633
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 87, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496634
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496635
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496637
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496638
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 91, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107496639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496642
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496643
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496646
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496514
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1', '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496516
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496518
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.162.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.162.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.162.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.162.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496524
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 9, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2732.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.172', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 172, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'D2', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496526
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496527
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496530
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107496531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1944.2732.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.a1', '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 2}
  • id: 107496532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 6, 'counter': 118, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.2732.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.125', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 125, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 107496533
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496535
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496536
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496537
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496538
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496539
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107496540
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.324.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496541
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.324.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.a1', '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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496543
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2732.486.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 107496546
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 3, 'counter': 130, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.2732.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.611', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 611, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}.S_3^2', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496547
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 131, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496548
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.648.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107496549
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 2, 'counter': 133, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1944.2732.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '972.477', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 477, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9^2:D_6', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107496550
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.972.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107496551
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2732.972.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107496552
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2732', 'ambient_counter': 2732, 'ambient_order': 1944, 'ambient_tex': 'C_2\\times C_9^2:D_6', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 1, 'counter': 136, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1944.2732.1944.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1944.2732', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2732, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_9^2:D_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C8'], '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: 107496634
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '54.h1'], 'contains': ['216.e1', '324.b1', '324.c1'], 'core': '972.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7325, -1, 6185, -1], 'generators': [972, 4, 684], 'label': '1944.2732.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '108.e1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496511
    {'ambient': '1944.2732', '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': '972.a1', 'complements': ['1944.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '3.b1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5126, 5571, 5244, 5176], 'generators': [1, 12, 216, 6, 4, 648, 36, 972], 'label': '1944.2732.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '972.477', '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': '972.477'}
  • id: 107496512
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1944.3714', 'aut_weyl_index': 36, 'centralizer': '324.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '12.c1', '18.b1', '18.c1', '18.d1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2396, 1476, 3953, 1285], 'generators': [7, 648, 36, 972, 4, 216], 'label': '1944.2732.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '12.c1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '972.477', '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': '324.125'}
  • id: 107496513
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 972, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.j1', '36.k1', '36.l1', '54.j1', '54.l1'], 'contains': ['216.a1', '324.h1', '324.i1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8232, -1, 7437, -1], 'generators': [978, 36, 648], 'label': '1944.2732.108.q1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.q1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107496514
    {'ambient': '1944.2732', 'aut_centralizer_order': 12, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1296, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '54.k1'], 'contains': ['216.f1', '324.i1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9670, -1, 9622, -1], 'generators': [978, 228, 684], 'label': '1944.2732.108.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '108.r1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 107496515
    {'ambient': '1944.2732', 'aut_centralizer_order': 324, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 17496, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '54.b1', '54.c1', '81.a1'], 'contains': ['324.a1', '324.d1', '486.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2310, -1, 2353, -1], 'generators': [7, 972, 36], 'label': '1944.2732.162.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '162.a1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496516
    {'ambient': '1944.2732', 'aut_centralizer_order': 324, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '54.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.c1', '54.d1', '54.e1', '54.f1', '81.a1'], 'contains': ['324.a1', '324.e1', '486.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2909, -1, 2775, -1], 'generators': [7, 972, 648], 'label': '1944.2732.162.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.b1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496517
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '162.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.b1', '54.d1', '81.b1'], 'contains': ['324.c1', '324.f1', '486.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [922, -1, 1027, -1], 'generators': [7, 972, 4], 'label': '1944.2732.162.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '162.c1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496518
    {'ambient': '1944.2732', 'aut_centralizer_order': 216, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 17496, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.g1', '54.h1', '81.b1'], 'contains': ['324.c1', '324.g1', '486.b1'], 'core': '972.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3643, -1, 4560, -1], 'generators': [6, 972, 4], 'label': '1944.2732.162.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.d1', 'projective_image': '972.477', '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': '2.1'}
  • id: 107496519
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.g1', '54.i1', '54.j1', '81.a1'], 'contains': ['324.a1', '324.h1', '486.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5065, -1, 5405, -1], 'generators': [6, 972, 648], 'label': '1944.2732.162.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '162.e1', 'projective_image': '972.477', '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': '6.1'}
  • id: 107496520
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.h1', '54.j1', '54.k1'], 'contains': ['324.b1', '324.i1', '486.b1'], 'core': '972.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8068, -1, 7633, -1], 'generators': [6, 972, 684], 'label': '1944.2732.162.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '162.f1', 'projective_image': '972.477', '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': '6.1'}
  • id: 107496521
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '6.1', 'aut_weyl_index': 11664, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['54.l1', '54.m1', '54.n1', '81.a1'], 'contains': ['324.d1', '324.e1', '324.h1', '486.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [1957, -1, 2603, -1], 'generators': [973, 6, 648], 'label': '1944.2732.162.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.g1', 'projective_image': '1944.2732', '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': '6.1'}
  • id: 107496522
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '486.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.n1', '81.b1'], 'contains': ['324.f1', '324.g1', '486.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [738, -1, 1363, -1], 'generators': [973, 6, 4], 'label': '1944.2732.162.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.h1', 'projective_image': '1944.2732', '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': '6.1'}
  • id: 107496523
    {'ambient': '1944.2732', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '972.a1', 'complements': ['324.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.b1', '12.d1', '18.f1', '18.g1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8326, 7180, 7595, 9178], 'generators': [6, 648, 36, 972, 12, 216], 'label': '1944.2732.6.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.b1', '12.d1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '972.477', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '972.477'}
  • id: 107496524
    {'ambient': '1944.2732', 'aut_centralizer_order': 8748, 'aut_label': '216.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 8748, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.b1', '72.c1', '72.d1', '72.e1', '108.a1', '108.j1', '108.q1'], 'contains': ['648.a1', '648.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6553, 4088, 6919, 3534], 'generators': [36, 648], 'label': '1944.2732.216.a1', 'mobius_quo': 1, 'mobius_sub': 216, 'normal_closure': '216.a1', 'normal_contained_in': ['72.a1', '72.b1', '108.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '1944.2732', 'quotient_action_image': '4.2', 'quotient_action_kernel': '54.15', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107496525
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.a1', '108.b1', '108.i1', '108.k1', '108.n1'], 'contains': ['648.a1', '648.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2827, -1, 4049, -1], 'generators': [4, 648], 'label': '1944.2732.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.b1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496526
    {'ambient': '1944.2732', 'aut_centralizer_order': 1944, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '6.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '108.c1', '108.h1', '108.l1', '108.p1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5532, -1, 4580, -1], 'generators': [48], 'label': '1944.2732.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.c1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496527
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.d1', '108.d1', '108.m1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4508, -1, 4925, -1], 'generators': [1348], 'label': '1944.2732.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '216.d1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107496528
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '108.e1', '108.o1'], 'contains': ['648.b1', '648.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7136, -1, 6185, -1], 'generators': [4, 684], 'label': '1944.2732.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '216.e1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496529
    {'ambient': '1944.2732', 'aut_centralizer_order': 1944, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '108.f1', '108.r1'], 'contains': ['648.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9346, -1, 9207, -1], 'generators': [912], 'label': '1944.2732.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '216.f1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496530
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1', '108.g1'], 'contains': ['648.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8737, -1, 8212, -1], 'generators': [268], 'label': '1944.2732.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '216.g1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107496531
    {'ambient': '1944.2732', 'aut_centralizer_order': 36, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 243, 'aut_weyl_group': '8.3', 'aut_weyl_index': 8748, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1'], 'contains': ['486.a1', '486.b1', '486.c1'], 'core': '972.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [1549, -1, 1547, -1], 'generators': [1, 6, 972], 'label': '1944.2732.243.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '243.a1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107496532
    {'ambient': '1944.2732', 'aut_centralizer_order': 17496, 'aut_label': '324.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.b1', '108.c1', '108.d1', '162.a1', '162.b1', '162.e1'], 'contains': ['648.a1', '972.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4324, 3302, 4752, 4383], 'generators': [972, 648], 'label': '1944.2732.324.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '324.a1', 'normal_contained_in': ['108.a1'], 'normal_contains': ['648.a1', '972.a1'], 'normalizer': '1.a1', 'old_label': '324.a1', 'projective_image': '972.477', 'quotient_action_image': '2.1', 'quotient_action_kernel': '162.43', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496533
    {'ambient': '1944.2732', 'aut_centralizer_order': 17496, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.e1', '108.f1', '108.g1', '162.f1'], 'contains': ['648.b1', '972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7789, -1, 7187, -1], 'generators': [972, 684], 'label': '1944.2732.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '324.b1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496534
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '648.603', 'aut_weyl_index': 108, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '12.h1', '18.a1', '18.b1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2954, -1, 3416, -1], 'generators': [7, 648, 4, 972, 48, 36], 'label': '1944.2732.6.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.c1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107496535
    {'ambient': '1944.2732', 'aut_centralizer_order': 3888, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1', '108.e1', '162.c1', '162.d1'], 'contains': ['648.c1', '972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2954, -1, 4234, -1], 'generators': [972, 4], 'label': '1944.2732.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '324.c1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496536
    {'ambient': '1944.2732', 'aut_centralizer_order': 324, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.h1', '108.i1', '108.j1', '162.a1', '162.g1'], 'contains': ['648.a1', '972.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2387, -1, 2783, -1], 'generators': [973, 648], 'label': '1944.2732.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.d1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496537
    {'ambient': '1944.2732', 'aut_centralizer_order': 324, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 11664, 'centralizer': '54.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.j1', '108.k1', '108.l1', '108.m1', '162.b1', '162.g1'], 'contains': ['648.a1', '972.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3235, -1, 3095, -1], 'generators': [973, 36], 'label': '1944.2732.324.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.e1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496538
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 11664, 'centralizer': '162.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.i1', '108.k1', '162.c1', '162.h1'], 'contains': ['648.c1', '972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1116, -1, 1946, -1], 'generators': [973, 4], 'label': '1944.2732.324.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.f1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496539
    {'ambient': '1944.2732', 'aut_centralizer_order': 216, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.n1', '108.o1', '162.d1', '162.h1'], 'contains': ['648.c1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [3588, -1, 4407, -1], 'generators': [978, 4], 'label': '1944.2732.324.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.g1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496540
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 11664, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.n1', '108.p1', '108.q1', '162.e1', '162.g1'], 'contains': ['648.a1', '972.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5065, -1, 5098, -1], 'generators': [978, 648], 'label': '1944.2732.324.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.h1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496541
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 11664, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.o1', '108.q1', '108.r1', '162.f1'], 'contains': ['648.b1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8167, -1, 7386, -1], 'generators': [978, 684], 'label': '1944.2732.324.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '324.i1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496542
    {'ambient': '1944.2732', 'aut_centralizer_order': 648, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '27.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.a1', '162.b1', '162.c1', '243.a1'], 'contains': ['972.a1', '972.b1'], 'core': '972.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2071, -1, 2598, -1], 'generators': [7, 972], 'label': '1944.2732.486.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '486.a1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107496543
    {'ambient': '1944.2732', 'aut_centralizer_order': 432, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '81.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.d1', '162.e1', '162.f1', '243.a1'], 'contains': ['972.a1', '972.c1'], 'core': '972.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3926, -1, 5282, -1], 'generators': [6, 972], 'label': '1944.2732.486.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '486.b1', 'projective_image': '972.477', '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: 107496544
    {'ambient': '1944.2732', 'aut_centralizer_order': 36, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': 972, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['162.g1', '162.h1', '243.a1'], 'contains': ['972.b1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [1725, -1, 2401, -1], 'generators': [973, 6], 'label': '1944.2732.486.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.c1', 'projective_image': '1944.2732', '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: 107496545
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '324.140', 'aut_weyl_index': 216, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['12.f1', '12.i1', '18.a1', '18.d1'], 'core': '36.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [4450, -1, 4750, -1], 'generators': [7, 648, 292, 972, 48, 36], 'label': '1944.2732.6.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '6.d1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 107496546
    {'ambient': '1944.2732', 'aut_centralizer_order': 17496, 'aut_label': '648.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['216.a1', '216.b1', '216.c1', '216.d1', '324.a1', '324.d1', '324.e1', '324.h1'], 'contains': ['1944.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4324, 3999, 4580, 3589], 'generators': [648], 'label': '1944.2732.648.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['216.a1', '324.a1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '1944.2732', 'quotient_action_image': '2.1', 'quotient_action_kernel': '324.147', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496547
    {'ambient': '1944.2732', 'aut_centralizer_order': 17496, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.e1', '216.f1', '216.g1', '324.b1', '324.i1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7789, -1, 7187, -1], 'generators': [684], 'label': '1944.2732.648.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '648.b1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496548
    {'ambient': '1944.2732', 'aut_centralizer_order': 3888, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 34992, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1', '216.e1', '324.c1', '324.f1', '324.g1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2979, -1, 4321, -1], 'generators': [4], 'label': '1944.2732.648.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '648.c1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496549
    {'ambient': '1944.2732', 'aut_centralizer_order': 69984, 'aut_label': '972.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 69984, 'centralizer': '1.a1', 'complements': ['2.c1'], 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.b1', '324.c1', '486.a1', '486.b1'], 'contains': ['1944.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3473, 3302, 4752, 4383], 'generators': [972], 'label': '1944.2732.972.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '972.a1', 'normal_contained_in': ['324.a1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '972.a1', 'projective_image': '972.477', 'quotient_action_image': '1.1', 'quotient_action_kernel': '972.477', 'quotient_action_kernel_order': 972, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107496550
    {'ambient': '1944.2732', 'aut_centralizer_order': 648, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 69984, 'centralizer': '27.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.d1', '324.e1', '324.f1', '486.a1', '486.c1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2218, -1, 2692, -1], 'generators': [973], 'label': '1944.2732.972.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '972.b1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107496551
    {'ambient': '1944.2732', 'aut_centralizer_order': 432, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '1.1', 'aut_weyl_index': 69984, 'centralizer': '81.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.g1', '324.h1', '324.i1', '486.b1', '486.c1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [3765, -1, 5011, -1], 'generators': [978], 'label': '1944.2732.972.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '972.c1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107496552
    {'ambient': '1944.2732', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.b1', '648.c1', '972.a1', '972.b1', '972.c1'], 'contains': [], 'core': '1944.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3548, 3656, 4666, 3986], 'generators': [], 'label': '1944.2732.1944.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1', 'normal_contained_in': ['648.a1', '972.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.a1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107496553
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '648.626', 'aut_weyl_index': 108, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.b1', '12.j1', '18.a1', '18.c1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [5353, -1, 5148, -1], 'generators': [7, 648, 216, 972, 48, 36], 'label': '1944.2732.6.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 107496554
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 36, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.a1', '12.k1', '18.e1', '18.f1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5803, -1, 6235, -1], 'generators': [6, 36, 648, 972, 4, 12], 'label': '1944.2732.6.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.f1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 107496555
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 36, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['12.e1', '12.l1', '18.e1', '18.g1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8928, -1, 8934, -1], 'generators': [6, 684, 648, 972, 4, 228], 'label': '1944.2732.6.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '6.g1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '162.5'}
  • id: 107496556
    {'ambient': '1944.2732', 'aut_centralizer_order': 1, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '5832.cf', 'aut_weyl_index': 12, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.d1', '12.j1', '18.h1'], 'core': '12.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [6248, -1, 5738, -1], 'generators': [973, 648, 36, 6, 12, 216], 'label': '1944.2732.6.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '324.36'}
  • id: 107496557
    {'ambient': '1944.2732', 'aut_centralizer_order': 3, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '972.429', 'aut_weyl_index': 72, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.c1', '12.h1', '12.k1', '18.h1', '18.i1'], 'core': '12.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [3352, -1, 4402, -1], 'generators': [973, 648, 36, 6, 4, 12], 'label': '1944.2732.6.i1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.i1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 107496558
    {'ambient': '1944.2732', 'aut_centralizer_order': 36, 'aut_label': '8.a1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '1944.3912', 'aut_weyl_index': 36, 'centralizer': '108.a1', 'complements': ['243.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['24.a1', '24.b1', '24.c1', '24.d1', '24.e1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7056, 5406, 7924, 5176], 'generators': [4, 48, 864], 'label': '1944.2732.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['24.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '1944.2732', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 107496559
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '324.a1', 'complements': ['972.c1', '972.b1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '6.a1', '6.c1', '6.d1', '6.e1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4545, 2731, 4817, 3004], 'generators': [7, 36, 216, 972, 648, 48, 4], 'label': '1944.2732.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '972.477', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '324.125'}
  • id: 107496560
    {'ambient': '1944.2732', 'aut_centralizer_order': 3, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1296.3034', 'aut_weyl_index': 54, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.a1', '18.c1', '18.f1', '18.h1', '27.a1', '27.b1'], 'core': '36.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [4035, -1, 2927, -1], 'generators': [1, 36, 648, 6, 972, 12], 'label': '1944.2732.9.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '972.477', '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': '108.16'}
  • id: 107496561
    {'ambient': '1944.2732', 'aut_centralizer_order': 9, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4321', 'aut_weyl_index': 81, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['18.b1', '18.e1', '18.i1', '27.a1', '27.c1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1713, -1, 2037, -1], 'generators': [1, 648, 36, 6, 972, 4], 'label': '1944.2732.9.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 107496562
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '324.167', 'aut_weyl_index': 216, 'centralizer': '108.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.a1', '6.c1', '6.f1'], 'contains': ['24.a1', '36.a1', '36.b1', '36.d1'], 'core': '12.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5084, 1476, 6048, 3401], 'generators': [972, 648, 4, 48, 36], 'label': '1944.2732.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '36.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 107496563
    {'ambient': '1944.2732', 'aut_centralizer_order': 324, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.122', 'aut_weyl_index': 324, 'centralizer': '12.b1', 'complements': ['162.h1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.b1', '6.e1'], 'contains': ['24.b1', '36.b1', '36.c1'], 'core': '12.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8167, 6420, 7566, 6819], 'generators': [972, 648, 48, 864, 36], 'label': '1944.2732.12.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.a1', '6.b1'], 'normal_contains': ['24.b1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '972.477', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496564
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '972.803', 'aut_weyl_index': 72, 'centralizer': '324.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.a1', '6.i1'], 'contains': ['24.a1', '36.g1', '36.h1', '36.i1'], 'core': '12.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2568, 3783, 4328, 1395], 'generators': [973, 648, 4, 12, 36], 'label': '1944.2732.12.c1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1', 'normal_contained_in': ['4.b1', '6.a1'], 'normal_contains': ['24.a1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '324.125'}
  • id: 107496565
    {'ambient': '1944.2732', 'aut_centralizer_order': 2, 'aut_label': '12.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '17496.rx', 'aut_weyl_index': 4, 'centralizer': '972.a1', 'complements': ['162.c1', '162.h1'], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.b1', '6.h1'], 'contains': ['24.b1', '36.k1', '36.l1'], 'core': '12.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [8580, 8524, 8195, 8231], 'generators': [978, 648, 12, 216, 36], 'label': '1944.2732.12.d1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1', 'normal_contained_in': ['4.c1', '6.b1'], 'normal_contains': ['24.b1'], 'normalizer': '1.a1', 'old_label': '12.d1', 'projective_image': '1944.2732', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '972.477'}
  • id: 107496566
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '324.167', 'aut_weyl_index': 216, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.g1'], 'contains': ['24.c1', '36.a1', '36.c1', '36.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8928, -1, 8934, -1], 'generators': [972, 648, 4, 912, 1332], 'label': '1944.2732.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.e1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '54.13'}
  • id: 107496567
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.52', 'aut_weyl_index': 432, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.d1'], 'contains': ['24.d1', '36.b1', '36.d1', '36.e1'], 'core': '36.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6057, -1, 7170, -1], 'generators': [972, 648, 868, 48, 36], 'label': '1944.2732.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.f1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '54.13'}
  • id: 107496568
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.52', 'aut_weyl_index': 432, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['24.e1', '36.c1', '36.d1', '36.e1'], 'core': '108.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7663, -1, 8507, -1], 'generators': [972, 648, 868, 912, 1332], 'label': '1944.2732.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '12.g1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 107496569
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '324.117', 'aut_weyl_index': 216, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.c1', '6.i1'], 'contains': ['24.a1', '36.f1', '36.g1'], 'core': '24.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3525, -1, 3644, -1], 'generators': [973, 36, 864, 648, 4], 'label': '1944.2732.12.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.h1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107496570
    {'ambient': '1944.2732', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '972.a1', 'complements': ['972.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '6.b1', '6.f1', '6.g1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7051, 5571, 7370, 7635], 'generators': [6, 36, 216, 972, 648, 4, 12], 'label': '1944.2732.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '972.477', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '972.477'}
  • id: 107496571
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '162.36', 'aut_weyl_index': 432, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.d1'], 'contains': ['24.d1', '36.f1', '36.i1'], 'core': '72.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [4736, -1, 4980, -1], 'generators': [973, 36, 864, 648, 664], 'label': '1944.2732.12.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '12.i1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 107496572
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '324.140', 'aut_weyl_index': 216, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.e1', '6.h1'], 'contains': ['24.b1', '36.f1', '36.h1'], 'core': '24.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5679, -1, 5256, -1], 'generators': [973, 36, 864, 648, 12], 'label': '1944.2732.12.j1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.j1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 107496573
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 72, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '6.f1', '6.i1'], 'contains': ['24.a1', '36.j1', '36.k1'], 'core': '24.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6907, -1, 6422, -1], 'generators': [978, 36, 4, 12, 648], 'label': '1944.2732.12.k1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.k1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 107496574
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 72, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.g1'], 'contains': ['24.c1', '36.j1', '36.l1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9505, -1, 9308, -1], 'generators': [978, 684, 4, 228, 648], 'label': '1944.2732.12.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '12.l1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '162.5'}
  • id: 107496575
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.48', 'aut_weyl_index': 972, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '6.d1', '6.e1', '9.a1'], 'contains': ['36.b1', '36.f1', '54.a1', '54.c1'], 'core': '36.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [4351, -1, 2972, -1], 'generators': [7, 648, 972, 48, 36], 'label': '1944.2732.18.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '972.477', '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': '12.4'}
  • id: 107496576
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.102', 'aut_weyl_index': 324, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.c1', '9.b1'], 'contains': ['36.a1', '36.g1', '54.b1', '54.c1', '54.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1358, -1, 1504, -1], 'generators': [7, 648, 972, 36, 4], 'label': '1944.2732.18.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.b1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107496577
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.111', 'aut_weyl_index': 324, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.e1', '9.a1'], 'contains': ['36.b1', '36.h1', '54.c1', '54.e1'], 'core': '36.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3451, -1, 3332, -1], 'generators': [7, 648, 972, 36, 216], 'label': '1944.2732.18.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.c1', 'projective_image': '972.477', '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': '36.4'}
  • id: 107496578
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 648, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.d1'], 'contains': ['36.d1', '36.i1', '54.c1', '54.f1'], 'core': '108.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2430, -1, 4704, -1], 'generators': [7, 648, 972, 36, 292], 'label': '1944.2732.18.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '18.d1', 'projective_image': '972.477', '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': '54.6'}
  • id: 107496579
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 486, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.g1', '9.b1'], 'contains': ['36.a1', '36.j1', '54.g1', '54.h1', '54.j1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6537, -1, 6770, -1], 'generators': [6, 648, 972, 4, 36], 'label': '1944.2732.18.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.e1', 'projective_image': '972.477', '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': '36.10'}
  • id: 107496580
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 36, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '6.f1', '9.a1'], 'contains': ['36.b1', '36.k1', '54.i1', '54.j1'], 'core': '36.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [6952, -1, 5621, -1], 'generators': [6, 36, 972, 12, 648], 'label': '1944.2732.18.f1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.f1', 'projective_image': '972.477', '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': '324.37'}
  • id: 107496581
    {'ambient': '1944.2732', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '17496.rx', 'aut_weyl_index': 4, 'centralizer': '972.a1', 'complements': ['972.a1', '972.b1', '972.c1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '6.h1', '6.i1'], 'core': '2.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [5126, 8397, 5669, 5176], 'generators': [973, 36, 216, 6, 648, 4, 12], 'label': '1944.2732.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '1944.2732', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '972.477'}
  • id: 107496582
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 36, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.g1'], 'contains': ['36.c1', '36.l1', '54.j1', '54.k1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9640, -1, 9656, -1], 'generators': [6, 684, 972, 228, 648], 'label': '1944.2732.18.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '18.g1', 'projective_image': '972.477', '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': '162.5'}
  • id: 107496583
    {'ambient': '1944.2732', 'aut_centralizer_order': 3, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '324.118', 'aut_weyl_index': 216, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.h1', '6.i1', '9.a1'], 'contains': ['36.f1', '36.h1', '36.k1', '54.l1', '54.m1'], 'core': '72.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [3791, -1, 3953, -1], 'generators': [973, 36, 6, 12, 648], 'label': '1944.2732.18.h1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.h1', 'projective_image': '1944.2732', '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': '108.16'}
  • id: 107496584
    {'ambient': '1944.2732', 'aut_centralizer_order': 9, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '216.159', 'aut_weyl_index': 324, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.i1', '9.b1'], 'contains': ['36.g1', '36.j1', '54.l1', '54.n1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1902, -1, 1864, -1], 'generators': [973, 648, 6, 4, 36], 'label': '1944.2732.18.i1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.i1', 'projective_image': '1944.2732', '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': '108.40'}
  • id: 107496585
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '24.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '324.167', 'aut_weyl_index': 216, 'centralizer': '108.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.a1', '12.c1', '12.h1', '12.k1'], 'contains': ['72.a1', '72.b1', '72.d1'], 'core': '24.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5855, 3783, 5642, 3942], 'generators': [4, 48], 'label': '1944.2732.24.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1', '12.c1'], 'normal_contains': ['72.a1', '72.b1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 107496586
    {'ambient': '1944.2732', 'aut_centralizer_order': 324, 'aut_label': '24.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '216.122', 'aut_weyl_index': 324, 'centralizer': '12.b1', 'complements': ['81.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1', '12.d1', '12.j1'], 'contains': ['72.b1', '72.c1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8190, 7217, 8212, 6819], 'generators': [48, 864], 'label': '1944.2732.24.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1', 'normal_contained_in': ['8.a1', '12.b1', '12.d1'], 'normal_contains': ['72.b1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '1944.2732', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496587
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '324.167', 'aut_weyl_index': 216, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.e1', '12.l1'], 'contains': ['72.a1', '72.c1', '72.e1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9008, -1, 9058, -1], 'generators': [4, 912], 'label': '1944.2732.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '24.c1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '54.13'}
  • id: 107496588
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.52', 'aut_weyl_index': 432, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.f1', '12.i1'], 'contains': ['72.b1', '72.d1', '72.e1'], 'core': '72.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6112, -1, 8003, -1], 'generators': [868, 48], 'label': '1944.2732.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.d1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '54.13'}
  • id: 107496589
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.52', 'aut_weyl_index': 432, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.g1'], 'contains': ['72.c1', '72.d1', '72.e1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7879, -1, 8420, -1], 'generators': [868, 912], 'label': '1944.2732.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.e1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 107496590
    {'ambient': '1944.2732', 'aut_centralizer_order': 9, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '288.889', 'aut_weyl_index': 243, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1'], 'contains': ['54.c1', '54.j1', '54.l1', '81.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1686, -1, 2212, -1], 'generators': [1, 648, 6, 972, 36], 'label': '1944.2732.27.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107496591
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '216.111', 'aut_weyl_index': 324, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.a1'], 'contains': ['54.a1', '54.e1', '54.i1', '54.m1', '81.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3883, -1, 2588, -1], 'generators': [1, 36, 6, 972, 12], 'label': '1944.2732.27.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '27.b1', 'projective_image': '972.477', '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': '18.1'}
  • id: 107496592
    {'ambient': '1944.2732', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '23328.gc', 'aut_weyl_index': 3, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.e1', '6.h1', '9.a1'], 'core': '6.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5691, -1, 5244, -1], 'generators': [1, 36, 216, 6, 648, 972, 12], 'label': '1944.2732.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '972.477', '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': '324.36'}
  • id: 107496593
    {'ambient': '1944.2732', 'aut_centralizer_order': 9, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '144.192', 'aut_weyl_index': 486, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.b1'], 'contains': ['54.b1', '54.d1', '54.g1', '54.n1', '81.a1', '81.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [910, -1, 1118, -1], 'generators': [1, 648, 6, 972, 4], 'label': '1944.2732.27.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '27.c1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107496594
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 972, 'centralizer': '36.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.e1', '18.b1', '18.e1'], 'contains': ['72.a1', '108.a1', '108.b1', '108.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6624, 2440, 6189, 2453], 'generators': [972, 4, 36, 648], 'label': '1944.2732.36.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1'], 'normal_contains': ['72.a1', '108.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '972.477', 'quotient_action_image': '36.10', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107496595
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1944, 'centralizer': '12.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.b1', '12.f1', '18.a1', '18.c1', '18.f1'], 'contains': ['72.b1', '108.a1', '108.c1'], 'core': '36.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5172, 4962, 5311, 5463], 'generators': [972, 48, 648, 36], 'label': '1944.2732.36.b1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.b1', 'normal_contained_in': ['12.a1', '12.b1'], 'normal_contains': ['72.b1', '108.a1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '972.477', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496596
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1944, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.e1', '12.g1', '18.g1'], 'contains': ['72.c1', '108.a1', '108.f1'], 'core': '108.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9354, -1, 9389, -1], 'generators': [972, 912, 648, 684], 'label': '1944.2732.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '36.c1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107496597
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 3888, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.f1', '12.g1', '18.d1'], 'contains': ['72.d1', '108.a1', '108.d1'], 'core': '108.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5577, -1, 7298, -1], 'generators': [972, 1348, 648, 36], 'label': '1944.2732.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.d1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107496598
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 3888, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.f1', '12.g1'], 'contains': ['72.e1', '108.a1', '108.g1'], 'core': '108.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8473, -1, 8727, -1], 'generators': [972, 268, 648, 684], 'label': '1944.2732.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.e1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107496599
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1944, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.h1', '12.i1', '12.j1', '18.a1', '18.h1'], 'contains': ['72.b1', '108.h1', '108.j1'], 'core': '72.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [4694, -1, 3546, -1], 'generators': [973, 864, 648, 36], 'label': '1944.2732.36.f1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.f1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496600
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.17', 'aut_weyl_index': 648, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '12.h1', '18.b1', '18.i1'], 'contains': ['72.a1', '108.i1', '108.j1', '108.k1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2064, -1, 1847, -1], 'generators': [973, 648, 4, 36], 'label': '1944.2732.36.g1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.g1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107496601
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 648, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '12.j1', '18.c1', '18.h1'], 'contains': ['72.b1', '108.j1', '108.l1'], 'core': '72.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3350, -1, 3872, -1], 'generators': [973, 648, 12, 36], 'label': '1944.2732.36.h1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.h1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 107496602
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1296, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '12.i1', '18.d1'], 'contains': ['72.d1', '108.j1', '108.m1'], 'core': '216.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3009, -1, 4414, -1], 'generators': [973, 648, 664, 36], 'label': '1944.2732.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '36.i1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 107496603
    {'ambient': '1944.2732', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.c1', '6.f1', '6.i1', '9.a1', '9.b1'], 'core': '6.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3352, -1, 3953, -1], 'generators': [1, 36, 12, 6, 648, 972, 4], 'label': '1944.2732.3.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '972.477', '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': '324.37'}
  • id: 107496604
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 972, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.k1', '12.l1', '18.e1', '18.i1'], 'contains': ['72.a1', '108.n1', '108.o1', '108.q1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7309, -1, 6578, -1], 'generators': [978, 4, 36, 648], 'label': '1944.2732.36.j1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.j1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107496605
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 72, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.k1', '18.f1', '18.h1'], 'contains': ['72.b1', '108.p1', '108.q1'], 'core': '72.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [7630, -1, 5889, -1], 'generators': [978, 12, 648, 36], 'label': '1944.2732.36.k1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.k1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 107496606
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 72, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.l1', '18.g1'], 'contains': ['72.c1', '108.q1', '108.r1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9767, -1, 9697, -1], 'generators': [978, 228, 648, 684], 'label': '1944.2732.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1', 'old_label': '36.l1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '162.5'}
  • id: 107496607
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5832, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '27.b1'], 'contains': ['108.c1', '108.h1', '162.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4381, -1, 2243, -1], 'generators': [7, 972, 48, 36], 'label': '1944.2732.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.a1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496608
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2916, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '27.c1'], 'contains': ['108.b1', '108.i1', '162.a1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1149, -1, 516, -1], 'generators': [7, 972, 36, 4], 'label': '1944.2732.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.b1', 'projective_image': '972.477', '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': '12.4'}
  • id: 107496609
    {'ambient': '1944.2732', 'aut_centralizer_order': 162, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2916, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.b1', '18.c1', '18.d1', '27.a1'], 'contains': ['108.a1', '108.j1', '162.a1', '162.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2317, -1, 2601, -1], 'generators': [7, 972, 36, 648], 'label': '1944.2732.54.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.c1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496610
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.102', 'aut_weyl_index': 324, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '27.c1'], 'contains': ['108.b1', '108.k1', '162.b1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [572, -1, 878, -1], 'generators': [7, 972, 4, 648], 'label': '1944.2732.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.d1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107496611
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 648, 'centralizer': '54.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '27.b1'], 'contains': ['108.c1', '108.l1', '162.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3846, -1, 3063, -1], 'generators': [7, 972, 216, 648], 'label': '1944.2732.54.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.e1', 'projective_image': '972.477', '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': '18.1'}
  • id: 107496612
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 648, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1'], 'contains': ['108.d1', '108.m1', '162.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2882, -1, 4143, -1], 'generators': [7, 972, 292, 648], 'label': '1944.2732.54.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '54.f1', 'projective_image': '972.477', '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': '54.6'}
  • id: 107496613
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2916, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.e1', '27.c1'], 'contains': ['108.b1', '108.n1', '162.d1', '162.e1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3376, -1, 4740, -1], 'generators': [6, 972, 4, 648], 'label': '1944.2732.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.g1', 'projective_image': '972.477', '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': '12.4'}
  • id: 107496614
    {'ambient': '1944.2732', 'aut_centralizer_order': 36, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1944.3912', 'aut_weyl_index': 36, 'centralizer': '108.a1', 'complements': ['486.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '12.a1', '12.b1', '12.e1', '12.f1', '12.g1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6788, 3314, 7144, 5176], 'generators': [972, 648, 36, 4, 48, 864], 'label': '1944.2732.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '12.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '972.477', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 107496615
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2916, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1'], 'contains': ['108.e1', '108.o1', '162.d1', '162.f1'], 'core': '972.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7529, -1, 6940, -1], 'generators': [6, 972, 4, 684], 'label': '1944.2732.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '54.h1', 'projective_image': '972.477', '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': '6.1'}
  • id: 107496616
    {'ambient': '1944.2732', 'aut_centralizer_order': 12, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '108.26', 'aut_weyl_index': 648, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.f1', '27.b1'], 'contains': ['108.c1', '108.p1', '162.e1'], 'core': '324.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6398, -1, 5009, -1], 'generators': [6, 972, 12, 36], 'label': '1944.2732.54.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.i1', 'projective_image': '972.477', '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': '18.1'}
  • id: 107496617
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 486, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '18.f1', '18.g1', '27.a1'], 'contains': ['108.a1', '108.q1', '162.e1', '162.f1'], 'core': '108.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7904, -1, 7693, -1], 'generators': [6, 972, 36, 648], 'label': '1944.2732.54.j1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.j1', 'projective_image': '972.477', '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': '36.10'}
  • id: 107496618
    {'ambient': '1944.2732', 'aut_centralizer_order': 12, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '108.26', 'aut_weyl_index': 648, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1'], 'contains': ['108.f1', '108.r1', '162.f1'], 'core': '972.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9829, -1, 9915, -1], 'generators': [6, 972, 228, 684], 'label': '1944.2732.54.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1', 'old_label': '54.k1', 'projective_image': '972.477', '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': '18.1'}
  • id: 107496619
    {'ambient': '1944.2732', 'aut_centralizer_order': 9, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '72.40', 'aut_weyl_index': 972, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.h1', '18.i1', '27.a1'], 'contains': ['108.j1', '108.q1', '162.g1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1999, -1, 2860, -1], 'generators': [973, 6, 36, 648], 'label': '1944.2732.54.l1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.l1', 'projective_image': '1944.2732', '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': '36.10'}
  • id: 107496620
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1296, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['18.h1', '27.b1'], 'contains': ['108.h1', '108.l1', '108.p1', '162.g1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4067, -1, 3277, -1], 'generators': [973, 6, 12, 36], 'label': '1944.2732.54.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.m1', 'projective_image': '1944.2732', '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': '18.1'}
  • id: 107496621
    {'ambient': '1944.2732', 'aut_centralizer_order': 9, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1944, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['18.i1', '27.c1'], 'contains': ['108.i1', '108.k1', '108.n1', '162.g1', '162.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [880, -1, 1175, -1], 'generators': [973, 6, 4, 648], 'label': '1944.2732.54.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.n1', 'projective_image': '1944.2732', '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': '36.10'}
  • id: 107496622
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 972, 'centralizer': '36.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.c1', '36.a1', '36.g1', '36.j1'], 'contains': ['216.a1', '216.b1', '216.e1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6656, 3682, 5923, 2762], 'generators': [4, 36, 648], 'label': '1944.2732.72.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.a1', 'normal_contained_in': ['24.a1', '36.a1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '1944.2732', 'quotient_action_image': '36.10', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107496623
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '72.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1944, 'centralizer': '12.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.b1', '24.d1', '36.b1', '36.f1', '36.h1', '36.k1'], 'contains': ['216.a1', '216.c1'], 'core': '72.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5418, 6027, 5654, 5463], 'generators': [48, 648], 'label': '1944.2732.72.b1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.b1', 'normal_contained_in': ['24.a1', '24.b1', '36.b1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '1944.2732', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496624
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1944, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.c1', '24.e1', '36.c1', '36.l1'], 'contains': ['216.a1', '216.f1'], 'core': '216.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9279, -1, 9058, -1], 'generators': [912, 648], 'label': '1944.2732.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '72.c1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107496625
    {'ambient': '1944.2732', 'aut_centralizer_order': 6, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '2916.ln', 'aut_weyl_index': 24, 'centralizer': '324.a1', 'complements': ['486.b1', '486.a1', '486.c1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.a1', '12.c1', '12.h1', '12.i1', '12.j1'], 'core': '4.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4838, 5418, 5491, 3346], 'generators': [973, 648, 36, 864, 4, 12], 'label': '1944.2732.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.a1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '1944.2732', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '324.125'}
  • id: 107496626
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 3888, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.d1', '24.e1', '36.d1', '36.i1'], 'contains': ['216.a1', '216.d1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5850, -1, 6837, -1], 'generators': [1348, 648], 'label': '1944.2732.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.d1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107496627
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 3888, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.d1', '24.e1', '36.e1'], 'contains': ['216.a1', '216.g1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8658, -1, 8212, -1], 'generators': [268, 648], 'label': '1944.2732.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.e1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107496628
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2916, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.a1', '27.b1', '27.c1'], 'contains': ['162.a1', '162.b1', '162.e1', '162.g1', '243.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [1937, -1, 1461, -1], 'generators': [1, 6, 972, 648], 'label': '1944.2732.81.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496629
    {'ambient': '1944.2732', 'aut_centralizer_order': 18, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '48.38', 'aut_weyl_index': 1458, 'centralizer': '486.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.c1'], 'contains': ['162.c1', '162.d1', '162.h1', '243.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [171, -1, 166, -1], 'generators': [1, 6, 972, 4], 'label': '1944.2732.81.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '81.b1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496630
    {'ambient': '1944.2732', 'aut_centralizer_order': 8748, 'aut_label': '108.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 8748, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.b1', '36.c1', '36.d1', '36.e1', '54.c1', '54.j1'], 'contains': ['216.a1', '324.a1', '324.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6788, 3150, 7163, 3964], 'generators': [972, 36, 648], 'label': '1944.2732.108.a1', 'mobius_quo': -1, 'mobius_sub': -54, 'normal_closure': '108.a1', 'normal_contained_in': ['36.a1', '36.b1'], 'normal_contains': ['216.a1', '324.a1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '972.477', 'quotient_action_image': '4.2', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107496631
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '54.b1', '54.d1', '54.g1'], 'contains': ['216.b1', '324.a1', '324.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2338, -1, 3908, -1], 'generators': [972, 4, 648], 'label': '1944.2732.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.b1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496632
    {'ambient': '1944.2732', 'aut_centralizer_order': 1944, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '6.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '54.a1', '54.e1', '54.i1'], 'contains': ['216.c1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5197, -1, 4829, -1], 'generators': [972, 48, 36], 'label': '1944.2732.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.c1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496633
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '36.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '54.f1'], 'contains': ['216.d1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4508, -1, 5213, -1], 'generators': [972, 1348, 36], 'label': '1944.2732.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '108.d1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107496635
    {'ambient': '1944.2732', 'aut_centralizer_order': 1944, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '54.k1'], 'contains': ['216.f1', '324.b1'], 'core': '972.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9128, -1, 9358, -1], 'generators': [972, 912, 684], 'label': '1944.2732.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '108.f1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496636
    {'ambient': '1944.2732', 'aut_centralizer_order': 2, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '17496.rx', 'aut_weyl_index': 4, 'centralizer': '972.a1', 'complements': ['486.a1', '486.c1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.c1'], 'contains': ['8.a1', '12.d1', '12.k1', '12.l1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [7362, 7814, 8005, 7293], 'generators': [978, 648, 36, 4, 12, 216], 'label': '1944.2732.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.d1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '1944.2732', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '972.477'}
  • id: 107496637
    {'ambient': '1944.2732', 'aut_centralizer_order': 972, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '36.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1'], 'contains': ['216.g1', '324.b1'], 'core': '972.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8842, -1, 8480, -1], 'generators': [972, 268, 684], 'label': '1944.2732.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '108.g1', 'projective_image': '972.477', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107496638
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.2', 'aut_weyl_index': 11664, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '54.a1', '54.m1'], 'contains': ['216.c1', '324.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4821, -1, 2968, -1], 'generators': [973, 864, 648], 'label': '1944.2732.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.h1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107496639
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.g1', '54.b1', '54.n1'], 'contains': ['216.b1', '324.d1', '324.f1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1196, -1, 1809, -1], 'generators': [973, 648, 4], 'label': '1944.2732.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.i1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496640
    {'ambient': '1944.2732', 'aut_centralizer_order': 162, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '36.g1', '36.h1', '36.i1', '54.c1', '54.l1'], 'contains': ['216.a1', '324.d1', '324.e1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3053, -1, 3236, -1], 'generators': [973, 648, 36], 'label': '1944.2732.108.j1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.j1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496641
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.17', 'aut_weyl_index': 648, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.g1', '54.d1', '54.n1'], 'contains': ['216.b1', '324.e1', '324.f1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [724, -1, 2080, -1], 'generators': [973, 4, 36], 'label': '1944.2732.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.k1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 107496642
    {'ambient': '1944.2732', 'aut_centralizer_order': 108, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1296, 'centralizer': '54.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.h1', '54.e1', '54.m1'], 'contains': ['216.c1', '324.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4215, -1, 3486, -1], 'generators': [973, 12, 36], 'label': '1944.2732.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.l1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 107496643
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1296, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.i1', '54.f1'], 'contains': ['216.d1', '324.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3311, -1, 3658, -1], 'generators': [973, 664, 36], 'label': '1944.2732.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '108.m1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 107496644
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.j1', '54.g1', '54.n1'], 'contains': ['216.b1', '324.g1', '324.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [3956, -1, 4234, -1], 'generators': [978, 4, 648], 'label': '1944.2732.108.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.n1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107496645
    {'ambient': '1944.2732', 'aut_centralizer_order': 54, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5832, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.j1', '54.h1'], 'contains': ['216.e1', '324.g1', '324.i1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [7663, -1, 6511, -1], 'generators': [978, 4, 684], 'label': '1944.2732.108.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '108.o1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107496646
    {'ambient': '1944.2732', 'aut_centralizer_order': 12, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1296, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.k1', '54.i1', '54.m1'], 'contains': ['216.c1', '324.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6134, -1, 5021, -1], 'generators': [978, 12, 36], 'label': '1944.2732.108.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.p1', 'projective_image': '1944.2732', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '18.1'}