Abstract group data - 1344.2922

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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': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 2, 6, 2, 12, 14, 12, 12], 'aut_gens': [[1, 2, 8, 48], [5, 694, 1240, 1104], [337, 1042, 1000, 1296], [5, 678, 584, 1104], [1, 2, 104, 624], [1013, 1014, 472, 432], [1, 674, 872, 48], [1, 690, 632, 1200], [5, 354, 8, 912]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 48, 'aut_perms': [213712654422506483601381041074396828297516173985376826277553, 5068682514933610350940093934666864801435214027478513957453902, 213709324575538845617006482550092612719195131416572271653400, 60472982422642370835649475799074632688142727432485793984, 11619005019796221621002176329636277389798699247406844139337785, 5695393245232552842624215788874951753190083496126552724717557, 4919470145911616507952876403552080375452188651088698697771357, 2541278032574330302296034994954911372504340295528906345549635], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 12, 1, 1], [2, 28, 1, 1], [2, 56, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 12, 1, 1], [4, 12, 2, 1], [4, 28, 1, 1], [4, 84, 2, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 56, 1, 1], [6, 56, 2, 1], [7, 2, 3, 1], [8, 8, 1, 1], [8, 168, 1, 1], [12, 4, 1, 2], [12, 56, 1, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 24, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [28, 2, 6, 1], [28, 4, 3, 1], [28, 12, 12, 1], [28, 24, 3, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 8, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 6896085666905541017, 'autcentquo_nilpotent': False, 'autcentquo_order': 4032, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 12, 1], [2, 28, 1], [2, 56, 1], [3, 2, 1], [4, 2, 2], [4, 12, 3], [4, 28, 1], [4, 84, 2], [6, 2, 1], [6, 4, 1], [6, 56, 3], [7, 2, 3], [8, 8, 1], [8, 168, 1], [12, 4, 2], [12, 56, 1], [14, 2, 3], [14, 4, 3], [14, 24, 3], [21, 4, 3], [24, 8, 2], [28, 2, 6], [28, 4, 3], [28, 12, 12], [28, 24, 3], [42, 4, 3], [42, 8, 3], [56, 8, 6], [84, 4, 6], [84, 8, 3], [168, 8, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.618', 'commutator_count': 1, 'commutator_label': '168.39', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2922, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 12, 1, 1], [2, 28, 1, 1], [2, 56, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 12, 1, 1], [4, 12, 2, 1], [4, 28, 1, 1], [4, 84, 1, 2], [6, 2, 1, 1], [6, 4, 1, 1], [6, 56, 1, 1], [6, 56, 2, 1], [7, 2, 3, 1], [8, 8, 1, 1], [8, 168, 1, 1], [12, 4, 1, 2], [12, 56, 1, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 24, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [28, 2, 6, 1], [28, 4, 3, 1], [28, 12, 12, 1], [28, 24, 3, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 8, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 21504, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, -1, 6]], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 2922, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [4, 4, 6, 14], 'inner_gens': [[1, 342, 344, 48], [1013, 2, 1048, 48], [1009, 354, 8, 1296], [1, 2, 104, 48]], 'inner_hash': 618, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_6:D_{28}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 96, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 38], [4, 46], [8, 7]], 'label': '1344.2922', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D12.D28', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 38, 'number_characteristic_subgroups': 56, 'number_conjugacy_classes': 99, 'number_divisions': 39, 'number_normal_subgroups': 58, 'number_subgroup_autclasses': 256, 'number_subgroup_classes': 292, 'number_subgroups': 2772, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 99], [3, 2], [4, 236], [6, 174], [7, 6], [8, 176], [12, 64], [14, 90], [21, 12], [24, 16], [28, 240], [42, 36], [56, 48], [84, 48], [168, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 340, 0], 'outer_gens': [[1, 2, 40, 48], [1, 674, 8, 48], [341, 2, 8, 48], [1, 2, 8, 240]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [720, 3628800, 40320, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 4], [6, 4], [8, 2], [12, 6], [24, 3], [48, 2]], 'representations': {'PC': {'code': 13483683933418879478189967466156833450451235647018171485149, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -3, -2, -2, -7, 2688, 5473, 41, 16226, 11011, 16779, 5459, 91, 652, 7805, 141, 8766, 166, 9247]}, 'Perm': {'d': 26, 'gens': [621574835364362295023737, 358765276816694, 4363767711508, 5776431824341, 5891871063997, 7296035791098, 6758061133824000, 16754357281155028254720000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{12}.D_{28}', 'transitive_degree': 336, '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: 115860202
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2922, 'group_order': 1344, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 115860213
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 2922, 'group_order': 1344, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 672, 'size': 1}
  • id: 115860224
    {'aut_label': '2B', 'centralizer': '2.f1.a1', 'counter': 3, 'group_counter': 2922, 'group_order': 1344, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 4, 'size': 2}
  • id: 115860235
    {'aut_label': '2C', 'centralizer': '12.k1.a1', 'counter': 4, 'group_counter': 2922, 'group_order': 1344, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 1011, 'size': 12}
  • id: 115860246
    {'aut_label': '2D', 'centralizer': '28.n1.a1', 'counter': 5, 'group_counter': 2922, 'group_order': 1344, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 936, 'size': 28}
  • id: 115860257
    {'aut_label': '2E', 'centralizer': '56.f1.a1', 'counter': 6, 'group_counter': 2922, 'group_order': 1344, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 745, 'size': 56}
  • id: 115860268
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 7, 'group_counter': 2922, 'group_order': 1344, 'label': '3A', 'order': 3, 'powers': [7, 1, 7], 'representative': 32, 'size': 2}
  • id: 115860279
    {'aut_label': '4A', 'centralizer': '2.e1.a1', 'counter': 8, 'group_counter': 2922, 'group_order': 1344, 'label': '4A', 'order': 4, 'powers': [2, 8, 8], 'representative': 1012, 'size': 2}
  • id: 115860290
    {'aut_label': '4B', 'centralizer': '2.c1.a1', 'counter': 9, 'group_counter': 2922, 'group_order': 1344, 'label': '4B', 'order': 4, 'powers': [2, 9, 9], 'representative': 336, 'size': 2}
  • id: 115860203
    {'aut_label': '4C', 'centralizer': '12.j1.a1', 'counter': 10, 'group_counter': 2922, 'group_order': 1344, 'label': '4C', 'order': 4, 'powers': [2, 10, 10], 'representative': 675, 'size': 12}
  • id: 115860204
    {'aut_label': '4D1', 'centralizer': '12.g1.a1', 'counter': 11, 'group_counter': 2922, 'group_order': 1344, 'label': '4D1', 'order': 4, 'powers': [3, 12, 12], 'representative': 6, 'size': 12}
  • id: 115860205
    {'aut_label': '4D1', 'centralizer': '12.g1.a1', 'counter': 12, 'group_counter': 2922, 'group_order': 1344, 'label': '4D-1', 'order': 4, 'powers': [3, 11, 11], 'representative': 2, 'size': 12}
  • id: 115860206
    {'aut_label': '4E', 'centralizer': '28.l1.a1', 'counter': 13, 'group_counter': 2922, 'group_order': 1344, 'label': '4E', 'order': 4, 'powers': [2, 13, 13], 'representative': 76, 'size': 28}
  • id: 115860207
    {'aut_label': '4F', 'centralizer': '84.b1.a1', 'counter': 14, 'group_counter': 2922, 'group_order': 1344, 'label': '4F', 'order': 4, 'powers': [2, 14, 14], 'representative': 1259, 'size': 84}
  • id: 115860208
    {'aut_label': '4F', 'centralizer': '84.b1.b1', 'counter': 15, 'group_counter': 2922, 'group_order': 1344, 'label': '4G', 'order': 4, 'powers': [2, 15, 15], 'representative': 251, 'size': 84}
  • id: 115860209
    {'aut_label': '6A', 'centralizer': '2.d1.a1', 'counter': 16, 'group_counter': 2922, 'group_order': 1344, 'label': '6A', 'order': 6, 'powers': [7, 2, 16], 'representative': 704, 'size': 2}
  • id: 115860210
    {'aut_label': '6B', 'centralizer': '4.c1.a1', 'counter': 17, 'group_counter': 2922, 'group_order': 1344, 'label': '6B', 'order': 6, 'powers': [7, 3, 17], 'representative': 20, 'size': 4}
  • id: 115860211
    {'aut_label': '6C', 'centralizer': '56.l1.a1', 'counter': 18, 'group_counter': 2922, 'group_order': 1344, 'label': '6C', 'order': 6, 'powers': [7, 5, 18], 'representative': 952, 'size': 56}
  • id: 115860212
    {'aut_label': '6D1', 'centralizer': '56.f1.a1', 'counter': 19, 'group_counter': 2922, 'group_order': 1344, 'label': '6D1', 'order': 6, 'powers': [7, 6, 19], 'representative': 761, 'size': 56}
  • id: 115860214
    {'aut_label': '6D1', 'centralizer': '56.f1.a1', 'counter': 20, 'group_counter': 2922, 'group_order': 1344, 'label': '6D-1', 'order': 6, 'powers': [7, 6, 20], 'representative': 729, 'size': 56}
  • id: 115860215
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 21, 'group_counter': 2922, 'group_order': 1344, 'label': '7A1', 'order': 7, 'powers': [22, 23, 1], 'representative': 768, 'size': 2}
  • id: 115860216
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 22, 'group_counter': 2922, 'group_order': 1344, 'label': '7A2', 'order': 7, 'powers': [23, 21, 1], 'representative': 192, 'size': 2}
  • id: 115860217
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 23, 'group_counter': 2922, 'group_order': 1344, 'label': '7A3', 'order': 7, 'powers': [21, 22, 1], 'representative': 960, 'size': 2}
  • id: 115860218
    {'aut_label': '8A', 'centralizer': '8.u1.a1', 'counter': 24, 'group_counter': 2922, 'group_order': 1344, 'label': '8A', 'order': 8, 'powers': [9, 24, 24], 'representative': 673, 'size': 8}
  • id: 115860219
    {'aut_label': '8B', 'centralizer': '168.r1.a1', 'counter': 25, 'group_counter': 2922, 'group_order': 1344, 'label': '8B', 'order': 8, 'powers': [8, 25, 25], 'representative': 106, 'size': 168}
  • id: 115860220
    {'aut_label': '12A', 'centralizer': '4.b1.a1', 'counter': 26, 'group_counter': 2922, 'group_order': 1344, 'label': '12A', 'order': 12, 'powers': [16, 8, 26], 'representative': 356, 'size': 4}
  • id: 115860221
    {'aut_label': '12B', 'centralizer': '4.f1.a1', 'counter': 27, 'group_counter': 2922, 'group_order': 1344, 'label': '12B', 'order': 12, 'powers': [16, 9, 27], 'representative': 1040, 'size': 4}
  • id: 115860222
    {'aut_label': '12C', 'centralizer': '56.l1.a1', 'counter': 28, 'group_counter': 2922, 'group_order': 1344, 'label': '12C', 'order': 12, 'powers': [16, 13, 28], 'representative': 764, 'size': 56}
  • id: 115860223
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 29, 'group_counter': 2922, 'group_order': 1344, 'label': '14A1', 'order': 14, 'powers': [21, 30, 2], 'representative': 1056, 'size': 2}
  • id: 115860225
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 30, 'group_counter': 2922, 'group_order': 1344, 'label': '14A3', 'order': 14, 'powers': [23, 31, 2], 'representative': 480, 'size': 2}
  • id: 115860226
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 31, 'group_counter': 2922, 'group_order': 1344, 'label': '14A5', 'order': 14, 'powers': [22, 29, 2], 'representative': 1248, 'size': 2}
  • id: 115860227
    {'aut_label': '14B1', 'centralizer': '4.d1.a1', 'counter': 32, 'group_counter': 2922, 'group_order': 1344, 'label': '14B1', 'order': 14, 'powers': [21, 33, 3], 'representative': 388, 'size': 4}
  • id: 115860228
    {'aut_label': '14B1', 'centralizer': '4.d1.a1', 'counter': 33, 'group_counter': 2922, 'group_order': 1344, 'label': '14B3', 'order': 14, 'powers': [23, 34, 3], 'representative': 1156, 'size': 4}
  • id: 115860229
    {'aut_label': '14B1', 'centralizer': '4.d1.a1', 'counter': 34, 'group_counter': 2922, 'group_order': 1344, 'label': '14B5', 'order': 14, 'powers': [22, 32, 3], 'representative': 580, 'size': 4}
  • id: 115860230
    {'aut_label': '14C1', 'centralizer': '24.j1.a1', 'counter': 35, 'group_counter': 2922, 'group_order': 1344, 'label': '14C1', 'order': 14, 'powers': [21, 36, 4], 'representative': 51, 'size': 24}
  • id: 115860231
    {'aut_label': '14C1', 'centralizer': '24.j1.a1', 'counter': 36, 'group_counter': 2922, 'group_order': 1344, 'label': '14C3', 'order': 14, 'powers': [23, 37, 4], 'representative': 147, 'size': 24}
  • id: 115860232
    {'aut_label': '14C1', 'centralizer': '24.j1.a1', 'counter': 37, 'group_counter': 2922, 'group_order': 1344, 'label': '14C5', 'order': 14, 'powers': [22, 35, 4], 'representative': 243, 'size': 24}
  • id: 115860233
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 38, 'group_counter': 2922, 'group_order': 1344, 'label': '21A1', 'order': 21, 'powers': [39, 22, 7], 'representative': 416, 'size': 4}
  • id: 115860234
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 39, 'group_counter': 2922, 'group_order': 1344, 'label': '21A2', 'order': 21, 'powers': [40, 23, 7], 'representative': 784, 'size': 4}
  • id: 115860236
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 40, 'group_counter': 2922, 'group_order': 1344, 'label': '21A4', 'order': 21, 'powers': [38, 21, 7], 'representative': 224, 'size': 4}
  • id: 115860237
    {'aut_label': '24A1', 'centralizer': '8.u1.a1', 'counter': 41, 'group_counter': 2922, 'group_order': 1344, 'label': '24A1', 'order': 24, 'powers': [27, 24, 41], 'representative': 1025, 'size': 8}
  • id: 115860238
    {'aut_label': '24A1', 'centralizer': '8.u1.a1', 'counter': 42, 'group_counter': 2922, 'group_order': 1344, 'label': '24A-1', 'order': 24, 'powers': [27, 24, 42], 'representative': 33, 'size': 8}
  • id: 115860239
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 43, 'group_counter': 2922, 'group_order': 1344, 'label': '28A1', 'order': 28, 'powers': [29, 44, 9], 'representative': 816, 'size': 2}
  • id: 115860240
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 44, 'group_counter': 2922, 'group_order': 1344, 'label': '28A3', 'order': 28, 'powers': [30, 46, 9], 'representative': 1104, 'size': 2}
  • id: 115860241
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 45, 'group_counter': 2922, 'group_order': 1344, 'label': '28A5', 'order': 28, 'powers': [31, 48, 9], 'representative': 48, 'size': 2}
  • id: 115860242
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 46, 'group_counter': 2922, 'group_order': 1344, 'label': '28A9', 'order': 28, 'powers': [31, 43, 9], 'representative': 624, 'size': 2}
  • id: 115860243
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 47, 'group_counter': 2922, 'group_order': 1344, 'label': '28A11', 'order': 28, 'powers': [30, 45, 9], 'representative': 912, 'size': 2}
  • id: 115860244
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 48, 'group_counter': 2922, 'group_order': 1344, 'label': '28A13', 'order': 28, 'powers': [29, 47, 9], 'representative': 1200, 'size': 2}
  • id: 115860245
    {'aut_label': '28B1', 'centralizer': '4.d1.a1', 'counter': 49, 'group_counter': 2922, 'group_order': 1344, 'label': '28B1', 'order': 28, 'powers': [29, 50, 8], 'representative': 148, 'size': 4}
  • id: 115860247
    {'aut_label': '28B1', 'centralizer': '4.d1.a1', 'counter': 50, 'group_counter': 2922, 'group_order': 1344, 'label': '28B3', 'order': 28, 'powers': [30, 51, 8], 'representative': 436, 'size': 4}
  • id: 115860248
    {'aut_label': '28B1', 'centralizer': '4.d1.a1', 'counter': 51, 'group_counter': 2922, 'group_order': 1344, 'label': '28B5', 'order': 28, 'powers': [31, 49, 8], 'representative': 724, 'size': 4}
  • id: 115860249
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 52, 'group_counter': 2922, 'group_order': 1344, 'label': '28C1', 'order': 28, 'powers': [32, 54, 11], 'representative': 194, 'size': 12}
  • id: 115860250
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 53, 'group_counter': 2922, 'group_order': 1344, 'label': '28C-1', 'order': 28, 'powers': [32, 55, 12], 'representative': 866, 'size': 12}
  • id: 115860251
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 54, 'group_counter': 2922, 'group_order': 1344, 'label': '28C3', 'order': 28, 'powers': [33, 58, 12], 'representative': 98, 'size': 12}
  • id: 115860252
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 55, 'group_counter': 2922, 'group_order': 1344, 'label': '28C-3', 'order': 28, 'powers': [33, 59, 11], 'representative': 770, 'size': 12}
  • id: 115860253
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 56, 'group_counter': 2922, 'group_order': 1344, 'label': '28C5', 'order': 28, 'powers': [34, 63, 11], 'representative': 962, 'size': 12}
  • id: 115860254
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 57, 'group_counter': 2922, 'group_order': 1344, 'label': '28C-5', 'order': 28, 'powers': [34, 62, 12], 'representative': 50, 'size': 12}
  • id: 115860255
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 58, 'group_counter': 2922, 'group_order': 1344, 'label': '28C9', 'order': 28, 'powers': [34, 53, 11], 'representative': 386, 'size': 12}
  • id: 115860256
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 59, 'group_counter': 2922, 'group_order': 1344, 'label': '28C-9', 'order': 28, 'powers': [34, 52, 12], 'representative': 54, 'size': 12}
  • id: 115860258
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 60, 'group_counter': 2922, 'group_order': 1344, 'label': '28C11', 'order': 28, 'powers': [33, 56, 12], 'representative': 434, 'size': 12}
  • id: 115860259
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 61, 'group_counter': 2922, 'group_order': 1344, 'label': '28C-11', 'order': 28, 'powers': [33, 57, 11], 'representative': 578, 'size': 12}
  • id: 115860260
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 62, 'group_counter': 2922, 'group_order': 1344, 'label': '28C13', 'order': 28, 'powers': [32, 60, 11], 'representative': 1154, 'size': 12}
  • id: 115860261
    {'aut_label': '28C1', 'centralizer': '12.g1.a1', 'counter': 63, 'group_counter': 2922, 'group_order': 1344, 'label': '28C-13', 'order': 28, 'powers': [32, 61, 12], 'representative': 198, 'size': 12}
  • id: 115860262
    {'aut_label': '28D1', 'centralizer': '24.j1.a1', 'counter': 64, 'group_counter': 2922, 'group_order': 1344, 'label': '28D1', 'order': 28, 'powers': [29, 65, 10], 'representative': 195, 'size': 24}
  • id: 115860263
    {'aut_label': '28D1', 'centralizer': '24.j1.a1', 'counter': 65, 'group_counter': 2922, 'group_order': 1344, 'label': '28D3', 'order': 28, 'powers': [30, 66, 10], 'representative': 99, 'size': 24}
  • id: 115860264
    {'aut_label': '28D1', 'centralizer': '24.j1.a1', 'counter': 66, 'group_counter': 2922, 'group_order': 1344, 'label': '28D5', 'order': 28, 'powers': [31, 64, 10], 'representative': 387, 'size': 24}
  • id: 115860265
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 67, 'group_counter': 2922, 'group_order': 1344, 'label': '42A1', 'order': 42, 'powers': [40, 29, 16], 'representative': 128, 'size': 4}
  • id: 115860266
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 68, 'group_counter': 2922, 'group_order': 1344, 'label': '42A5', 'order': 42, 'powers': [38, 31, 16], 'representative': 496, 'size': 4}
  • id: 115860267
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 69, 'group_counter': 2922, 'group_order': 1344, 'label': '42A11', 'order': 42, 'powers': [39, 30, 16], 'representative': 1072, 'size': 4}
  • id: 115860269
    {'aut_label': '42B1', 'centralizer': '8.a1.a1', 'counter': 70, 'group_counter': 2922, 'group_order': 1344, 'label': '42B1', 'order': 42, 'powers': [38, 34, 17], 'representative': 212, 'size': 8}
  • id: 115860270
    {'aut_label': '42B1', 'centralizer': '8.a1.a1', 'counter': 71, 'group_counter': 2922, 'group_order': 1344, 'label': '42B5', 'order': 42, 'powers': [39, 33, 17], 'representative': 404, 'size': 8}
  • id: 115860271
    {'aut_label': '42B1', 'centralizer': '8.a1.a1', 'counter': 72, 'group_counter': 2922, 'group_order': 1344, 'label': '42B11', 'order': 42, 'powers': [40, 32, 17], 'representative': 116, 'size': 8}
  • id: 115860272
    {'aut_label': '56A1', 'centralizer': '8.u1.a1', 'counter': 73, 'group_counter': 2922, 'group_order': 1344, 'label': '56A1', 'order': 56, 'powers': [43, 74, 24], 'representative': 913, 'size': 8}
  • id: 115860273
    {'aut_label': '56A1', 'centralizer': '8.u1.a1', 'counter': 74, 'group_counter': 2922, 'group_order': 1344, 'label': '56A3', 'order': 56, 'powers': [44, 76, 24], 'representative': 385, 'size': 8}
  • id: 115860274
    {'aut_label': '56A1', 'centralizer': '8.u1.a1', 'counter': 75, 'group_counter': 2922, 'group_order': 1344, 'label': '56A5', 'order': 56, 'powers': [45, 78, 24], 'representative': 1201, 'size': 8}
  • id: 115860275
    {'aut_label': '56A1', 'centralizer': '8.u1.a1', 'counter': 76, 'group_counter': 2922, 'group_order': 1344, 'label': '56A9', 'order': 56, 'powers': [46, 73, 24], 'representative': 145, 'size': 8}
  • id: 115860276
    {'aut_label': '56A1', 'centralizer': '8.u1.a1', 'counter': 77, 'group_counter': 2922, 'group_order': 1344, 'label': '56A11', 'order': 56, 'powers': [47, 75, 24], 'representative': 961, 'size': 8}
  • id: 115860277
    {'aut_label': '56A1', 'centralizer': '8.u1.a1', 'counter': 78, 'group_counter': 2922, 'group_order': 1344, 'label': '56A13', 'order': 56, 'powers': [48, 77, 24], 'representative': 433, 'size': 8}
  • id: 115860278
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 79, 'group_counter': 2922, 'group_order': 1344, 'label': '84A1', 'order': 84, 'powers': [67, 43, 27], 'representative': 752, 'size': 4}
  • id: 115860280
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 80, 'group_counter': 2922, 'group_order': 1344, 'label': '84A5', 'order': 84, 'powers': [68, 45, 27], 'representative': 928, 'size': 4}
  • id: 115860281
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 81, 'group_counter': 2922, 'group_order': 1344, 'label': '84A11', 'order': 84, 'powers': [69, 47, 27], 'representative': 1216, 'size': 4}
  • id: 115860282
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 82, 'group_counter': 2922, 'group_order': 1344, 'label': '84A13', 'order': 84, 'powers': [67, 48, 27], 'representative': 1328, 'size': 4}
  • id: 115860283
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 83, 'group_counter': 2922, 'group_order': 1344, 'label': '84A19', 'order': 84, 'powers': [68, 46, 27], 'representative': 272, 'size': 4}
  • id: 115860284
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 84, 'group_counter': 2922, 'group_order': 1344, 'label': '84A25', 'order': 84, 'powers': [69, 44, 27], 'representative': 560, 'size': 4}
  • id: 115860285
    {'aut_label': '84B1', 'centralizer': '8.a1.a1', 'counter': 85, 'group_counter': 2922, 'group_order': 1344, 'label': '84B1', 'order': 84, 'powers': [67, 49, 26], 'representative': 68, 'size': 8}
  • id: 115860286
    {'aut_label': '84B1', 'centralizer': '8.a1.a1', 'counter': 86, 'group_counter': 2922, 'group_order': 1344, 'label': '84B5', 'order': 84, 'powers': [68, 51, 26], 'representative': 260, 'size': 8}
  • id: 115860287
    {'aut_label': '84B1', 'centralizer': '8.a1.a1', 'counter': 87, 'group_counter': 2922, 'group_order': 1344, 'label': '84B11', 'order': 84, 'powers': [69, 50, 26], 'representative': 164, 'size': 8}
  • id: 115860288
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 88, 'group_counter': 2922, 'group_order': 1344, 'label': '168A1', 'order': 168, 'powers': [79, 73, 41], 'representative': 209, 'size': 8}
  • id: 115860289
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 89, 'group_counter': 2922, 'group_order': 1344, 'label': '168A-1', 'order': 168, 'powers': [79, 73, 42], 'representative': 225, 'size': 8}
  • id: 115860291
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 90, 'group_counter': 2922, 'group_order': 1344, 'label': '168A5', 'order': 168, 'powers': [80, 75, 42], 'representative': 81, 'size': 8}
  • id: 115860292
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 91, 'group_counter': 2922, 'group_order': 1344, 'label': '168A-5', 'order': 168, 'powers': [80, 75, 41], 'representative': 65, 'size': 8}
  • id: 115860293
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 92, 'group_counter': 2922, 'group_order': 1344, 'label': '168A11', 'order': 168, 'powers': [81, 77, 42], 'representative': 609, 'size': 8}
  • id: 115860294
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 93, 'group_counter': 2922, 'group_order': 1344, 'label': '168A-11', 'order': 168, 'powers': [81, 77, 41], 'representative': 593, 'size': 8}
  • id: 115860295
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 94, 'group_counter': 2922, 'group_order': 1344, 'label': '168A13', 'order': 168, 'powers': [82, 78, 41], 'representative': 1169, 'size': 8}
  • id: 115860296
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 95, 'group_counter': 2922, 'group_order': 1344, 'label': '168A-13', 'order': 168, 'powers': [82, 78, 42], 'representative': 1185, 'size': 8}
  • id: 115860297
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 96, 'group_counter': 2922, 'group_order': 1344, 'label': '168A19', 'order': 168, 'powers': [83, 76, 41], 'representative': 401, 'size': 8}
  • id: 115860298
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 97, 'group_counter': 2922, 'group_order': 1344, 'label': '168A-19', 'order': 168, 'powers': [83, 76, 42], 'representative': 417, 'size': 8}
  • id: 115860299
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 98, 'group_counter': 2922, 'group_order': 1344, 'label': '168A25', 'order': 168, 'powers': [84, 74, 41], 'representative': 113, 'size': 8}
  • id: 115860300
    {'aut_label': '168A1', 'centralizer': '8.u1.a1', 'counter': 99, 'group_counter': 2922, 'group_order': 1344, 'label': '168A-25', 'order': 168, 'powers': [84, 74, 42], 'representative': 129, 'size': 8}
• 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: 5733325
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5733336
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5733347
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -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: 5733358
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -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: 5733359
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.1e', '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, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 5733360
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.1f', '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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 5733361
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.1g', '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, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -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: 5733362
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.1h', '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, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -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: 5733363
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, 2, -1, 2, 2, 0, 0, 0, 2, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5733326
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 2, 2, -2, 0, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 2, -2, 0, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733327
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -2, 0, 2, -2, 2, 0, 0, 0, 2, 0, 0, 2, -2, -2, 0, 0, 2, 2, 2, 0, 0, -2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733328
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 2, 0, 2, -2, 2, 0, 0, 0, -2, 0, 0, 2, -2, 2, 0, 0, 2, 2, 2, 0, 0, -2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733329
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 0, 0, 2, 2, -2, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 2, -2, 0, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733330
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, -2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, -2, -2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733331
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 2, -2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, -2, -2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733332
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -2, -2, -1, 2, 2, 0, 0, 0, -2, 0, 0, -1, -1, 1, 1, 1, 2, 2, 2, 2, 0, -1, -1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5733333
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -2, 2, -1, 2, 2, 0, 0, 0, -2, 0, 0, -1, -1, 1, -1, -1, 2, 2, 2, -2, 0, -1, -1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5733334
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, -2, -1, 2, 2, 0, 0, 0, 2, 0, 0, -1, -1, -1, 1, 1, 2, 2, 2, -2, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5733335
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2k', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, -4, 0, -4, 0, -2, -4, 4, 0, 0, 0, 4, 0, 0, -2, 2, 2, 0, 0, 4, 4, 4, 0, 0, 2, -2, -2, 4, 4, 4, -4, -4, -4, 0, 0, 0, -2, -2, -2, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733337
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2l', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 4, 0, -2, -4, 4, 0, 0, 0, -4, 0, 0, -2, 2, -2, 0, 0, 4, 4, 4, 0, 0, 2, -2, 2, 4, 4, 4, -4, -4, -4, 0, 0, 0, -2, -2, -2, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733344
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, -2, 4, -4, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 4, 4, 4, 0, 0, -2, 2, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, -2, -2, -2, 0, 0, -4, -4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733345
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, -2, -4, -4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 4, 4, 4, 0, 0, 2, 2, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, -2, -2, -2, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733338
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2m', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 6, 6, 0, 0, 0, -1, -1, -1, 6, 0, 6, 6, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 5733339
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2n', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 0, 0, 6, 6, 6, -6, -6, -6, 0, 0, 0, 6, 6, 0, 0, 0, -1, -1, -1, 6, 0, 6, 6, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 5733340
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2o', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, -6, 0, 0, 6, 6, 6, 6, -6, 6, 0, 0, 0, 6, 6, 0, 0, 0, -1, -1, -1, -6, 0, 6, 6, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -6, -6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 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: 5733341
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2p', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 6, 6, 6, -6, 6, -6, 0, 0, 0, 6, 6, 0, 0, 0, -1, -1, -1, -6, 0, 6, 6, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -6, -6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 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: 5733346
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4c', 'multiplicity': 2, 'nt': [16, 162], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 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: 5733356
    {'cdim': 8, 'counter': 38, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.8a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 5733342
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2q', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 0, 0, 12, 12, -12, 0, 12, 0, 0, 0, 0, 12, -12, 0, 0, 0, -2, -2, -2, 0, 0, 12, -12, 0, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733343
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.2r', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, -12, 12, 0, 0, 12, 12, -12, 0, -12, 0, 0, 0, 0, 12, -12, 0, 0, 0, -2, -2, -2, 0, 0, 12, -12, 0, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733348
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4d', 'multiplicity': 3, 'nt': [21, 8], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, -6, 12, 12, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, -2, -2, -2, 12, 0, -6, -6, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 1, 1, 1, -6, -6, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5733349
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4e', 'multiplicity': 3, 'nt': [28, 18], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 0, 0, 12, -12, 12, 0, 0, 0, 0, 0, 0, 12, -12, 0, 0, 0, -2, -2, -2, 0, 0, -12, 12, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, -2, -2, -2, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733350
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4f', 'multiplicity': 3, 'nt': [28, 18], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 12, -12, -12, 0, 0, 0, 0, 0, 0, 12, 12, 0, 0, 0, -2, -2, -2, 0, 0, -12, -12, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733351
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4g', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, -6, 12, 12, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, -2, -2, -2, -12, 0, -6, -6, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 1, 1, 1, 6, 6, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5733352
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4h', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, -24, 0, 0, 0, -12, -24, 24, 0, 0, 0, 0, 0, 0, -12, 12, 0, 0, 0, -4, -4, -4, 0, 0, 12, -12, 0, -4, -4, -4, 4, 4, 4, 0, 0, 0, 2, 2, 2, 0, 0, -4, -4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733353
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4i', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, -24, 0, 0, 0, -12, 24, -24, 0, 0, 0, 0, 0, 0, -12, 12, 0, 0, 0, -4, -4, -4, 0, 0, -12, 12, 0, -4, -4, -4, 4, 4, 4, 0, 0, 0, 2, 2, 2, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733354
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4j', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, 24, 0, 0, 0, -12, -24, -24, 0, 0, 0, 0, 0, 0, -12, -12, 0, 0, 0, -4, -4, -4, 0, 0, 12, 12, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 2, 2, 2, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5733355
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.4k', 'multiplicity': 12, 'nt': [112, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 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: 5733357
    {'cdim': 8, 'counter': 39, 'faithful': True, 'group': '1344.2922', 'group_order': 1344, 'image': None, 'label': '1344.2922.8b', 'multiplicity': 6, 'nt': [336, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• 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: 11520858
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1344, 'label': '1344.2922.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 11520869
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 672, 'label': '1344.2922.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 11520880
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 672, 'label': '1344.2922.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 11520891
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 672, 'label': '1344.2922.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 11520902
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 672, 'label': '1344.2922.1e', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 11520913
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 672, 'label': '1344.2922.1f', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 11520924
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 672, 'label': '1344.2922.1g', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 11520935
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 672, 'label': '1344.2922.1h', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 11520946
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 224, 'label': '1344.2922.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 11520859
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 336, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 168, 'label': '1344.2922.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520860
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 336, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1.a1', 'kernel_order': 168, 'label': '1344.2922.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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: 11520861
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 336, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1.a1', 'kernel_order': 168, 'label': '1344.2922.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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: 11520862
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 336, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 168, 'label': '1344.2922.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520863
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 336, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 168, 'label': '1344.2922.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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: 11520864
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 336, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 168, 'label': '1344.2922.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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: 11520865
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 112, 'label': '1344.2922.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 11520866
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 112, 'label': '1344.2922.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 11520867
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 112, 'label': '1344.2922.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 11520868
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 112, 'counter': 19, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 56, 'label': '1344.2922.2k1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]]]}
  • id: 11520870
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 112, 'counter': 20, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 56, 'label': '1344.2922.2k2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]]]}
  • id: 11520871
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 112, 'counter': 21, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 56, 'label': '1344.2922.2l1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]]]}
  • id: 11520872
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 112, 'counter': 22, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 56, 'label': '1344.2922.2l2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]]]}
  • id: 11520873
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 23, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.2922.2m1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 11520874
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  • id: 11520875
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 25, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.2922.2m3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 11520876
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 26, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.2922.2n1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 11520877
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 27, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.2922.2n2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 11520878
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 28, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.c1.a1', 'kernel_order': 48, 'label': '1344.2922.2n3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 11520879
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 29, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.2922.2o1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 11520881
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 30, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.2922.2o2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 11520882
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 31, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.2922.2o3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 11520883
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 32, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.2922.2p1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 11520884
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 33, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.2922.2p2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 11520885
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 34, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.2922.2p3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 11520886
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 35, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.2922.2q1', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 11520887
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 36, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.2922.2q2', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 11520888
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 37, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.2922.2q3', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 11520889
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 38, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.2922.2q4', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 11520890
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 39, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.2922.2q5', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 11520892
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 40, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.2922.2q6', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]]]}
  • id: 11520893
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 41, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 24, 'label': '1344.2922.2r1', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 11520894
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 42, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 24, 'label': '1344.2922.2r2', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 11520895
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 43, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 24, 'label': '1344.2922.2r3', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 11520896
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 44, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 24, 'label': '1344.2922.2r4', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 11520897
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 45, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 24, 'label': '1344.2922.2r5', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]]]}
  • id: 11520898
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 46, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.b1.a1', 'kernel_order': 24, 'label': '1344.2922.2r6', 'nt': [28, 10], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 11520899
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 56, 'counter': 47, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 28, 'label': '1344.2922.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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: 11520900
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 56, 'counter': 48, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 28, 'label': '1344.2922.4b', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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: 11520901
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 42, 'counter': 49, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '64.135', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 21, 'label': '1344.2922.4c1', 'nt': [16, 162], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 11520903
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 42, 'counter': 50, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '64.135', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 21, 'label': '1344.2922.4c2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 11520904
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 51, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.2922.4d1', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 0]], [[-2, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 11520905
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 52, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.2922.4d2', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 11520906
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 53, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.2922.4d3', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 11520907
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 54, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.c1.a1', 'kernel_order': 12, 'label': '1344.2922.4e1', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -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]]]}
  • id: 11520908
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 55, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.c1.a1', 'kernel_order': 12, 'label': '1344.2922.4e2', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -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]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -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]]]}
  • id: 11520909
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 56, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.c1.a1', 'kernel_order': 12, 'label': '1344.2922.4e3', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -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]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520910
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 57, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 12, 'label': '1344.2922.4f1', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -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]]]}
  • id: 11520911
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 58, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 12, 'label': '1344.2922.4f2', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -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]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -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]]]}
  • id: 11520912
    {'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 59, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '112.31', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1.a1', 'kernel_order': 12, 'label': '1344.2922.4f3', 'nt': [28, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -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]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520914
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 60, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.2922.4g1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 0]], [[2, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 11520915
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 61, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.2922.4g2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 11520916
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 62, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.2922.4g3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 11520917
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 63, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.2922.4h1', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -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]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]]]}
  • id: 11520918
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 64, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.2922.4h2', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -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]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]]]}
  • id: 11520919
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 65, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.2922.4h3', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -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]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]]]}
  • id: 11520920
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 66, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.2922.4h4', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -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]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]]]}
  • id: 11520921
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 67, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.2922.4h5', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-2, 0], [-4, 7]], [[2, 0], [4, 7]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]]]}
  • id: 11520922
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 68, 'cyclotomic_n': 21, 'dim': 4, 'faithful': False, 'field': [1, -2, 5, 0, 3, -1, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.161', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.2922.4h6', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[-2, 6], [-2, -6]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[2, 0], [4, 7]], [[-2, 0], [-4, 7]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 9], [-2, -9]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[1, 3], [1, 4], [2, 10], [-1, -10]], [[-1, 3], [-1, 4], [-2, 10], [1, -10]], [[-2, 0], [1, 1], [2, 2], [-2, 3], [2, 5], [-1, 6], [-2, 7], [1, 8], [-2, 10], [2, -10]], [[2, 0], [-1, 1], [-2, 2], [2, 3], [-2, 5], [1, 6], [2, 7], [-1, 8], [2, 10], [-2, -10]], [[1, 0], [-1, 1], [-2, 2], [1, 3], [-1, 4], [-2, 5], [1, 6], [-1, 8], [-1, -10]], [[-1, 0], [1, 1], [2, 2], [-1, 3], [1, 4], [2, 5], [-1, 6], [1, 8], [1, -10]]]}
  • id: 11520923
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 69, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.b1.a1', 'kernel_order': 4, 'label': '1344.2922.4i1', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -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, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 11520925
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 70, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.b1.a1', 'kernel_order': 4, 'label': '1344.2922.4i2', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -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, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 11520926
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 71, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.b1.a1', 'kernel_order': 4, 'label': '1344.2922.4i3', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -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, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]]]}
  • id: 11520927
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 72, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.b1.a1', 'kernel_order': 4, 'label': '1344.2922.4i4', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -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, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]]]}
  • id: 11520928
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 73, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.b1.a1', 'kernel_order': 4, 'label': '1344.2922.4i5', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]]]}
  • id: 11520929
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 74, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.b1.a1', 'kernel_order': 4, 'label': '1344.2922.4i6', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]]]}
  • id: 11520930
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 75, 'cyclotomic_n': 84, 'dim': 4, 'faithful': False, 'field': [189, 0, 126, 0, 21, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.150', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.2922.4j1', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 18], [-2, -18]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[-2, 12], [-2, -12]], [[2, 18], [2, -18]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]]]}
  • id: 11520931
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 76, 'cyclotomic_n': 84, 'dim': 4, 'faithful': False, 'field': [189, 0, 126, 0, 21, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.150', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.2922.4j2', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[-2, 18], [-2, -18]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[-2, 12], [-2, -12]], [[2, 18], [2, -18]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]]]}
  • id: 11520932
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 77, 'cyclotomic_n': 84, 'dim': 4, 'faithful': False, 'field': [189, 0, 126, 0, 21, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.150', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.2922.4j3', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[0, 0]], [[0, 0]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[2, 18], [2, -18]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]]]}
  • id: 11520933
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 78, 'cyclotomic_n': 84, 'dim': 4, 'faithful': False, 'field': [189, 0, 126, 0, 21, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.150', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.2922.4j4', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[-2, 6], [-2, -6]], [[2, 12], [2, -12]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[0, 0]], [[0, 0]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[2, 18], [2, -18]], [[2, 18], [2, -18]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]]]}
  • id: 11520934
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 79, 'cyclotomic_n': 84, 'dim': 4, 'faithful': False, 'field': [189, 0, 126, 0, 21, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.150', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.2922.4j5', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 18], [-2, -18]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[2, 18], [2, -18]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 18], [1, -18]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]]]}
  • id: 11520936
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 80, 'cyclotomic_n': 84, 'dim': 4, 'faithful': False, 'field': [189, 0, 126, 0, 21, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '336.150', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.2922.4j6', 'nt': [84, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 18], [-2, -18]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[-2, 18], [-2, -18]], [[2, 12], [2, -12]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 18], [1, -18]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[2, 18], [2, -18]], [[2, 6], [2, -6]], [[-2, 12], [-2, -12]], [[-2, 12], [-2, -12]], [[2, 6], [2, -6]], [[2, 18], [2, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 18], [1, -18]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 6], [1, -6]], [[-1, 12], [-1, -12]], [[1, 18], [1, -18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[-1, 18], [-1, -18]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 18], [-1, -18]], [[-1, 6], [-1, -6]], [[1, 12], [1, -12]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]], [[-1, 5], [1, 9], [-1, 19], [-2, 23]], [[1, 5], [-1, 9], [1, 19], [2, 23]], [[-1, 1], [-2, 3], [1, 7], [1, 9], [1, 11], [-1, 13], [3, 17], [1, 19], [-1, 23]], [[1, 1], [2, 3], [-1, 7], [-1, 9], [-1, 11], [1, 13], [-3, 17], [-1, 19], [1, 23]], [[3, 1], [-1, 5], [-1, 7], [1, 11], [-1, 13], [-2, 15], [-1, 17], [1, 21], [1, 23]], [[-3, 1], [1, 5], [1, 7], [-1, 11], [1, 13], [2, 15], [1, 17], [-1, 21], [-1, 23]]]}
  • id: 11520937
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 81, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k1', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520947
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 90, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k10', 'nt': [112, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[0, 0]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520948
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 91, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k11', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520949
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 92, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k12', 'nt': [112, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[0, 0]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520938
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 82, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k2', 'nt': [112, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[0, 0]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520939
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 83, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k3', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520940
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 84, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k4', 'nt': [112, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[0, 0]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520941
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 85, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k5', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[-2, 3], [-2, -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]]]}
  • id: 11520942
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 86, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k6', 'nt': [112, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[0, 0]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[-2, 3], [-2, -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]]]}
  • id: 11520943
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 87, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k7', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[2, 3], [2, -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]]]}
  • id: 11520944
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 88, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k8', 'nt': [112, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[0, 0]], [[-2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[2, 3], [2, -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]]]}
  • id: 11520945
    {'center': '224.a1.a1', 'center_index': 224, 'center_order': 6, 'counter': 89, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '448.361', 'image_order': 448, 'indicator': 0, 'kernel': '448.a1.a1', 'kernel_order': 3, 'label': '1344.2922.4k9', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 7]], [[0, 0]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 5], [-1, 6], [1, 7], [-1, 8], [-1, 9], [1, 11]], [[1, 0], [-2, 2], [1, 4], [-1, 5], [-1, 6], [1, 8], [-1, 9], [-1, 10]], [[-1, 3], [-1, 4], [-1, 10], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [1, 5], [1, 6], [-1, 8], [1, 9], [1, 10]], [[1, 3], [-1, 5], [1, 6], [1, 7], [1, 8], [-1, 9], [1, 11]], [[-1, 3], [1, 5], [1, 6], [-1, 7], [1, 8], [1, 9], [-1, 11]], [[1, 0], [-2, 2], [1, 4], [1, 5], [-1, 6], [1, 8], [1, 9], [-1, 10]], [[-1, 3], [1, 4], [1, 10], [-1, 11]], [[-1, 0], [2, 2], [-1, 4], [-1, 5], [1, 6], [-1, 8], [-1, 9], [1, 10]], [[1, 3], [1, 4], [1, 10], [1, 11]], [[-1, 3], [1, 5], [-1, 6], [-1, 7], [-1, 8], [1, 9], [-1, 11]], [[1, 3], [-1, 4], [-1, 10], [1, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520950
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 14, 'counter': 93, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '192.760', 'image_order': 192, 'indicator': -1, 'kernel': '192.a1.a1', 'kernel_order': 7, 'label': '1344.2922.8a', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 11520951
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 94, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.2922', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.2922.8b1', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[4, 4], [4, -4]], [[-4, 6], [-4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4], [-4, -4]], [[4, 2], [4, -2]], [[4, 6], [4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[-4, 5], [-4, -5]], [[4, 1], [4, -1]], [[-4, 3], [-4, -3]], [[4, 3], [4, -3]], [[-4, 1], [-4, -1]], [[4, 5], [4, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520952
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 95, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.2922', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.2922.8b2', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2], [-4, -2]], [[4, 4], [4, -4]], [[-4, 6], [-4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 4], [-4, -4]], [[4, 2], [4, -2]], [[4, 6], [4, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[4, 5], [4, -5]], [[-4, 1], [-4, -1]], [[4, 3], [4, -3]], [[-4, 3], [-4, -3]], [[4, 1], [4, -1]], [[-4, 5], [-4, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520953
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 96, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.2922', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.2922.8b3', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 6], [-4, -6]], [[-4, 2], [-4, -2]], [[4, 4], [4, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 6], [4, -6]], [[-4, 4], [-4, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[-4, 3], [-4, -3]], [[-4, 5], [-4, -5]], [[4, 5], [4, -5]], [[4, 3], [4, -3]], [[4, 1], [4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 3], [-2, -3]], [[2, 3], [2, -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]]]}
  • id: 11520954
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 97, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.2922', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.2922.8b4', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 6], [-4, -6]], [[-4, 2], [-4, -2]], [[4, 4], [4, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 2], [4, -2]], [[4, 6], [4, -6]], [[-4, 4], [-4, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[4, 3], [4, -3]], [[4, 5], [4, -5]], [[-4, 5], [-4, -5]], [[-4, 3], [-4, -3]], [[-4, 1], [-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 3], [2, -3]], [[-2, 3], [-2, -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]]]}
  • id: 11520955
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 98, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.2922', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.2922.8b5', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4], [4, -4]], [[-4, 6], [-4, -6]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 6], [4, -6]], [[-4, 4], [-4, -4]], [[4, 2], [4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[-4, 3], [-4, -3]], [[4, 5], [4, -5]], [[4, 1], [4, -1]], [[-4, 1], [-4, -1]], [[-4, 5], [-4, -5]], [[4, 3], [4, -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]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 11520956
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 99, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.2922', 'group_counter': 2922, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.2922', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.2922.8b6', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4], [4, -4]], [[-4, 6], [-4, -6]], [[-4, 2], [-4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 6], [4, -6]], [[-4, 4], [-4, -4]], [[4, 2], [4, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[0, 0]], [[0, 0]], [[4, 3], [4, -3]], [[-4, 5], [-4, -5]], [[-4, 1], [-4, -1]], [[4, 1], [4, -1]], [[4, 5], [4, -5]], [[-4, 3], [-4, -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]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 72205326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1344, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '1344.2922.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1344.2922', 'subgroup_hash': 2922, 'subgroup_order': 1344, 'subgroup_tex': 'D_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1130', 'subgroup_hash': 1130, 'subgroup_order': 672, 'subgroup_tex': 'D_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.442', 'subgroup_hash': 442, 'subgroup_order': 672, 'subgroup_tex': 'D_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 672, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.205', 'subgroup_hash': 205, 'subgroup_order': 672, 'subgroup_tex': 'D_{12}:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 672, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.801', 'subgroup_hash': 801, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.94', 'subgroup_hash': 94, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.508', 'subgroup_hash': 508, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.245', 'subgroup_hash': 245, 'subgroup_order': 672, 'subgroup_tex': 'C_4.D_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 72205607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 224, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '1344.2922.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '448.361', 'subgroup_hash': 361, 'subgroup_order': 448, 'subgroup_tex': 'D_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 336, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.187', 'subgroup_hash': 187, 'subgroup_order': 336, 'subgroup_tex': 'D_{12}:C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.177', 'subgroup_hash': 177, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 72205349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.176', 'subgroup_hash': 176, 'subgroup_order': 336, 'subgroup_tex': 'C_6\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 336, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.81', 'subgroup_hash': 81, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.194', 'subgroup_hash': 194, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 336, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.110', 'subgroup_hash': 110, 'subgroup_order': 336, 'subgroup_tex': '\\OD_{16}\\times C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 72205393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.96', 'subgroup_hash': 96, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.153', 'subgroup_hash': 153, 'subgroup_order': 336, 'subgroup_tex': 'D_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.153', 'subgroup_hash': 153, 'subgroup_order': 336, 'subgroup_tex': 'D_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.42', 'subgroup_hash': 42, 'subgroup_order': 336, 'subgroup_tex': 'C_6.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.42', 'subgroup_hash': 42, 'subgroup_order': 336, 'subgroup_tex': 'C_6.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.138', 'subgroup_hash': 138, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 72205460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.140', 'subgroup_hash': 140, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.145', 'subgroup_hash': 145, 'subgroup_order': 336, 'subgroup_tex': 'D_{12}:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.29', 'subgroup_hash': 29, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.137', 'subgroup_hash': 137, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 168, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.61', 'subgroup_hash': 61, 'subgroup_order': 336, 'subgroup_tex': 'C_3\\times D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 72205515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 168, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.32', 'subgroup_hash': 32, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 168, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.60', 'subgroup_hash': 60, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 224, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', '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': '224.103', 'subgroup_hash': 103, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.186', 'subgroup_hash': 186, 'subgroup_order': 224, 'subgroup_tex': 'D_4.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.144', 'subgroup_hash': 144, 'subgroup_order': 224, 'subgroup_tex': 'D_4:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 112, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.53', 'subgroup_hash': 53, 'subgroup_order': 224, 'subgroup_tex': 'D_4:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.11', 'subgroup_hash': 11, 'subgroup_order': 224, 'subgroup_tex': 'D_{28}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '224.70', 'subgroup_hash': 70, 'subgroup_order': 224, 'subgroup_tex': 'C_4^2:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 112, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '224.30', 'subgroup_hash': 30, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1344.2922.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.760', 'subgroup_hash': 760, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 168, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.39', 'subgroup_hash': 39, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 72205550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.37', 'subgroup_hash': 37, 'subgroup_order': 168, 'subgroup_tex': 'C_{42}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.37', 'subgroup_hash': 37, 'subgroup_order': 168, 'subgroup_tex': 'C_{42}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 168, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.31', 'subgroup_hash': 31, 'subgroup_order': 168, 'subgroup_tex': 'C_7\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 168, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.29', 'subgroup_hash': 29, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.24', 'subgroup_hash': 24, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 84, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.33', 'subgroup_hash': 33, 'subgroup_order': 168, 'subgroup_tex': 'D_6:C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.54', 'subgroup_hash': 54, 'subgroup_order': 168, 'subgroup_tex': 'C_6\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 84, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.32', 'subgroup_hash': 32, 'subgroup_order': 168, 'subgroup_tex': 'C_6:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.15', 'subgroup_hash': 15, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 84, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.13', 'subgroup_hash': 13, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.13', 'subgroup_hash': 13, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.25', 'subgroup_hash': 25, 'subgroup_order': 168, 'subgroup_tex': 'C_{12}\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.12', 'subgroup_hash': 12, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.26', 'subgroup_hash': 26, 'subgroup_order': 168, 'subgroup_tex': 'C_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205573
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.5', 'subgroup_hash': 5, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.34', 'subgroup_hash': 34, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205576
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 84, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.6', 'subgroup_hash': 6, 'subgroup_order': 168, 'subgroup_tex': 'C_{168}', 'supersolvable': True, 'sylow': 0}
  • id: 72205577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.18', 'subgroup_hash': 18, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 42, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.8.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.18', 'subgroup_hash': 18, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 112, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', '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': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 112, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', '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': '112.29', 'subgroup_hash': 29, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 112, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 28, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 28, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 56, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.40', 'subgroup_hash': 40, 'subgroup_order': 112, 'subgroup_tex': 'D_4:C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.13', 'subgroup_hash': 13, 'subgroup_order': 112, 'subgroup_tex': 'D_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '112.13', 'subgroup_hash': 13, 'subgroup_order': 112, 'subgroup_tex': 'D_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205588
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.19', 'subgroup_hash': 19, 'subgroup_order': 112, 'subgroup_tex': 'C_4\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.9', 'subgroup_hash': 9, 'subgroup_order': 112, 'subgroup_tex': 'C_7:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 28, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.32', 'subgroup_hash': 32, 'subgroup_order': 112, 'subgroup_tex': 'D_4:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 28, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.14', 'subgroup_hash': 14, 'subgroup_order': 112, 'subgroup_tex': 'C_7:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 28, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.33', 'subgroup_hash': 33, 'subgroup_order': 112, 'subgroup_tex': 'Q_8\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 56, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.6', 'subgroup_hash': 6, 'subgroup_order': 112, 'subgroup_tex': 'D_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 72205598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 28, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.16', 'subgroup_hash': 16, 'subgroup_order': 112, 'subgroup_tex': 'Q_8:D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 56, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 96, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.32', 'subgroup_hash': 32, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.217', 'subgroup_hash': 217, 'subgroup_order': 96, 'subgroup_tex': 'D_4.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 72205602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.139', 'subgroup_hash': 139, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 72205603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.183', 'subgroup_hash': 183, 'subgroup_order': 96, 'subgroup_tex': 'D_8:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 72205604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.44', 'subgroup_hash': 44, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.14.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.143', 'subgroup_hash': 143, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.14.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.31', 'subgroup_hash': 31, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 84, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 72205609
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 84, 'counter': 91, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 72205610
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 92, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 72205611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 42, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205614
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 42, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205615
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205616
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205617
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205330
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 21, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1344.2922.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.135', 'subgroup_hash': 135, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 2}
  • id: 72205332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 56, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205339
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 28, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 28, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.10', 'subgroup_hash': 10, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205356
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 28, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.1', 'subgroup_hash': 1, 'subgroup_order': 56, 'subgroup_tex': 'C_7:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205358
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 28, 'counter': 128, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 72205359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 14, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.24.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 48, 'counter': 131, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 48, 'counter': 132, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 48, 'counter': 133, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.24', 'subgroup_hash': 24, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 72205366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 72205367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 72205368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.10', 'subgroup_hash': 10, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 72205375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.15', 'subgroup_hash': 15, 'subgroup_order': 48, 'subgroup_tex': 'C_3:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.28.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205383
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 150, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['S', 'L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 72205384
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 21, 'counter': 151, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 72205385
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 21, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205386
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205387
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 72205389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 16, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.42.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.42.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.42.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 162, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205397
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 163, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205398
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 28, 'counter': 164, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205399
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205400
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 14, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205402
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 14, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205403
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205405
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205406
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.48.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205409
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 174, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 72205410
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 24, 'counter': 175, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 176, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 177, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 12, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 72205417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 12, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 12, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 72205423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 72205424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 72205425
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205427
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205433
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205436
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 12, 'counter': 199, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.56.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 72205439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.56.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205441
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 21, 'counter': 202, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '1344.2922.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.135', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 135, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4.D_4', 'simple': False, 'solvable': True, 'special_labels': ['L3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 72205442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 16, 'counter': 203, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 8, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205451
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 72205452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.84.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 72205463
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 222, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.144', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 144, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_4', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205464
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 7, 'counter': 223, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205465
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 7, 'counter': 224, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 72205466
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205467
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 7, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 72205468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 227, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 72205469
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 228, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205470
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 229, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205472
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 6, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 72205473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 72205474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 72205475
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 6, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205476
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.112.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 72205477
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205478
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 72205480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 72205481
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 3, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.112.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 8, 'counter': 240, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': 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': 0}
  • id: 72205487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205506
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 261, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.168.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205509
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 4, 'counter': 264, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.168.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.168.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 72205512
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 7, 'counter': 267, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1344.2922.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.760', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 760, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}.D_4', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 72205513
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 6, 'counter': 268, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.77', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 77, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:D_{28}', '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: 72205514
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 3, 'counter': 269, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.224.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 72205516
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 3, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.224.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 72205517
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 271, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.224.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 72205518
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 272, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.224.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 72205519
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 273, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2922.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.150', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 150, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 72205520
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 274, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.149', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 149, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205521
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 275, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.161', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205522
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.336.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': 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: 72205523
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.336.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': 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: 72205524
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.336.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': 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: 72205525
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 279, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.336.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205527
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 280, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.336.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205528
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 281, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.336.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 282, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.336.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.336.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': 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: 72205531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2922.336.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': 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: 72205532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.336.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 72205533
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 3, 'counter': 286, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '1344.2922.448.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '448.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '448.361', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 361, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 448, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4.D_{28}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 72205534
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 287, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2922.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.618', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 618, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_{28}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 72205535
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.672.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, '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: 72205536
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.672.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, '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: 72205538
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.672.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, '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: 72205539
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2922.672.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, '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: 72205540
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2922', 'ambient_counter': 2922, 'ambient_order': 1344, 'ambient_tex': 'D_{12}.D_{28}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 1, 'counter': 292, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1344.2922.1344.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1344.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1344.2922', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2922, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}.D_{28}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', '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: 72205326
    {'ambient': '1344.2922', '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': '672.a1.a1', 'complements': ['1344.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 16, 24, 672, 192, 2, 340], 'label': '1344.2922.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205327
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.e1.a1', '8.g1.a1', '8.l1.a1', '12.e1.a1', '28.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 16, 336, 192, 340, 672], 'label': '1344.2922.4.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.e1.a1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205328
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '48.j1.a1', '112.j1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25, 16, 192, 4], 'label': '1344.2922.16.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '16.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205329
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '48.j1.a2', '112.j1.a2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25, 16, 192, 676], 'label': '1344.2922.16.j1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.b1', 'old_label': '16.j1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205330
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1'], 'contains': ['32.b1.a1', '48.k1.a1', '112.k1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2, 4, 16, 192], 'label': '1344.2922.16.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205331
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.c1.a1', '42.d1.a1', '42.e1.a1', '42.f1.a1', '42.g1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 2, 24], 'label': '1344.2922.21.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '21.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205332
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.e1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '168.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 192, 672, 336], 'label': '1344.2922.24.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '48.c1.a1', '48.b1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205333
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1', '12.j1.a1', '12.o1.a1'], 'contains': ['48.c1.a1', '48.e1.a1', '168.m1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24, 672, 192, 336], 'label': '1344.2922.24.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.d1.a1', '12.a1.a1'], 'normal_contains': ['48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205334
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.a1.a1', '12.k1.a1', '12.q1.a1'], 'contains': ['48.c1.a1', '48.h1.a1', '168.s1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1036, 672, 192, 336], 'label': '1344.2922.24.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.f1.a1', '12.a1.a1'], 'normal_contains': ['48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205335
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.g1.a1', '168.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 192, 672, 676], 'label': '1344.2922.24.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205336
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.a1.a1', '12.d1.a1', '12.d1.b1'], 'contains': ['48.a1.a1', '48.e1.a1', '48.h1.a1', '168.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [676, 672, 192, 24], 'label': '1344.2922.24.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205337
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.b1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.j1.a1', '48.j1.a2', '168.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25, 672, 192, 676], 'label': '1344.2922.24.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '24.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205338
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.f1.a1', '8.h1.a1', '8.n1.a1', '12.a1.a1', '28.e1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 192, 336, 16, 24, 672], 'label': '1344.2922.4.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.a1', '8.f1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205339
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.f1.a1', '12.f1.b1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '168.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 192, 4, 672], 'label': '1344.2922.24.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205340
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.d1.a1', '12.f1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.i1.a1', '168.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [11, 672, 192, 676], 'label': '1344.2922.24.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205341
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.d1.b1', '12.f1.b1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.i1.b1', '168.f1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [347, 672, 192, 676], 'label': '1344.2922.24.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205342
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.d1.a1', '12.j1.a1', '12.l1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.i1.a1', '168.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 672, 192, 360], 'label': '1344.2922.24.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205343
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '12.d1.b1', '12.j1.a1', '12.l1.a1'], 'contains': ['48.d1.a1', '48.e1.a1', '48.i1.b1', '168.g1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 672, 192, 24], 'label': '1344.2922.24.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205344
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.e1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.g1.a1', '168.h1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 192, 672, 336], 'label': '1344.2922.24.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205345
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.d1.a1', '12.k1.a1', '12.l1.a1'], 'contains': ['48.d1.a1', '48.h1.a1', '48.i1.a1', '168.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 672, 192, 1036], 'label': '1344.2922.24.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205346
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '12.d1.b1', '12.k1.a1', '12.l1.a1'], 'contains': ['48.d1.a1', '48.h1.a1', '48.i1.b1', '168.i1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 672, 192, 28], 'label': '1344.2922.24.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205347
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.e1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.b1.a1', '48.d1.a1', '168.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [339, 192, 672, 340], 'label': '1344.2922.24.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205348
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.a1.a1', '12.l1.a1', '12.n1.a1'], 'contains': ['48.b1.a1', '48.e1.a1', '48.h1.a1', '168.k1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [340, 672, 192, 24], 'label': '1344.2922.24.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205349
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.p1.a1', '8.q1.a1', '12.b1.a1', '28.g1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25, 192, 336, 16, 340, 672], 'label': '1344.2922.4.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205350
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.d1.a1', '12.j1.a1', '12.n1.a1'], 'contains': ['48.e1.a1', '48.g1.a1', '48.i1.a1', '168.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 672, 192, 24], 'label': '1344.2922.24.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205351
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.d1.b1', '12.j1.a1', '12.n1.a1'], 'contains': ['48.e1.a1', '48.g1.a1', '48.i1.b1', '168.l1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 672, 192, 360], 'label': '1344.2922.24.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205352
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.b1.a1', '12.m1.a1', '12.p1.a1'], 'contains': ['48.b1.a1', '48.f1.a1', '168.n1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25, 672, 192, 340], 'label': '1344.2922.24.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205353
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.b1.a1', '12.o1.a1', '12.q1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '168.o1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25, 672, 192, 336], 'label': '1344.2922.24.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205354
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.e1.a1', '12.n1.a1', '12.p1.a1'], 'contains': ['48.b1.a1', '48.g1.a1', '168.p1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 192, 672, 340], 'label': '1344.2922.24.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205355
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '12.h1.a1', '12.l1.a1', '12.n1.a1'], 'contains': ['48.b1.a1', '48.i1.a1', '48.i1.b1', '168.q1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [11, 672, 192, 340], 'label': '1344.2922.24.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205356
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '12.i1.a1', '12.m1.a1', '12.p1.a1'], 'contains': ['48.b1.a1', '168.r1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [10, 672, 192, 340], 'label': '1344.2922.24.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205357
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '12.h1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.c1.a1', '48.i1.a1', '48.i1.b1', '168.t1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [11, 672, 192, 336], 'label': '1344.2922.24.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205358
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '12.c1.a1', '12.o1.a1', '12.q1.a1'], 'contains': ['48.c1.a1', '168.u1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 336, 672, 192], 'label': '1344.2922.24.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205359
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '12.d1.a1', '12.k1.a1', '12.n1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.i1.a1', '168.v1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 672, 192, 28], 'label': '1344.2922.24.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205360
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '12.g1.a1', '28.b1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 16, 192, 4, 336, 672], 'label': '1344.2922.4.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205361
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.b1', '12.d1.b1', '12.k1.a1', '12.n1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.i1.b1', '168.v1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 672, 192, 1036], 'label': '1344.2922.24.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205362
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1', '14.b1.a1', '14.c1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.c1.a1', '56.d1.a1', '56.j1.a1', '84.c1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 16, 340, 336, 672], 'label': '1344.2922.28.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.a1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.b1.a1', '56.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205363
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.a1.a1', '14.e1.a1', '14.f1.a1'], 'contains': ['56.a1.a1', '56.g1.a1', '84.g1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 16, 336, 4, 672], 'label': '1344.2922.28.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.d1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205364
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '14.a1.a1', '14.d1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.u1.a1', '84.a1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 340, 16, 336], 'label': '1344.2922.28.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.c1.a1', 'normal_contained_in': ['4.f1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205365
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '14.b1.a1'], 'contains': ['56.d1.a1', '56.e1.a1', '56.h1.a1', '56.i1.a1', '56.k1.a1', '56.m1.a1', '56.v1.a1', '84.b1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 16, 676, 24, 672], 'label': '1344.2922.28.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205366
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '14.b1.a1'], 'contains': ['56.d1.a1', '56.e1.a1', '56.h1.b1', '56.i1.b1', '56.k1.b1', '56.m1.b1', '56.v1.b1', '84.b1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [339, 16, 676, 24, 672], 'label': '1344.2922.28.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205367
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.b1.a1', '14.d1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.e1.a1', '56.l1.a1', '56.n1.a1', '56.s1.a1', '84.d1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [340, 672, 24, 336, 16], 'label': '1344.2922.28.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205368
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '14.f1.a1'], 'contains': ['56.f1.a1', '56.g1.a1', '56.h1.a1', '84.e1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [361, 16, 2, 676, 672], 'label': '1344.2922.28.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '28.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205369
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '14.f1.a1'], 'contains': ['56.f1.a1', '56.g1.a1', '56.h1.b1', '84.e1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [25, 16, 2, 676, 672], 'label': '1344.2922.28.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '28.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205370
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.c1.a1', '14.d1.a1', '14.f1.a1'], 'contains': ['56.a1.a1', '56.f1.a1', '56.o1.a1', '56.p1.a1', '84.f1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [25, 672, 340, 336, 16], 'label': '1344.2922.28.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205371
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.r1.a1', '8.t1.a1', '12.h1.a1', '28.h1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [11, 192, 336, 672, 340, 16], 'label': '1344.2922.4.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205372
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.b1.a1', '14.f1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.h1.a1', '56.h1.b1', '56.q1.a1', '56.t1.a1', '84.h1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [11, 16, 340, 336, 672], 'label': '1344.2922.28.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205373
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '14.c1.a1', '14.e1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.r1.a1', '84.i1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [10, 16, 336, 340, 672], 'label': '1344.2922.28.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205374
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '14.b1.a1'], 'contains': ['56.i1.a1', '56.i1.b1', '56.j1.a1', '56.m1.a1', '56.m1.b1', '56.n1.a1', '56.t1.a1', '84.j1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 16, 24, 336, 672], 'label': '1344.2922.28.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205375
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '14.b1.a1'], 'contains': ['56.j1.a1', '56.k1.a1', '56.k1.b1', '56.s1.a1', '56.t1.a1', '56.v1.a1', '56.v1.b1', '84.k1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 16, 1036, 336, 672], 'label': '1344.2922.28.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205376
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '14.b1.a1'], 'contains': ['56.b1.a1', '56.i1.a1', '56.i1.b1', '56.k1.a1', '56.k1.b1', '56.l1.a1', '56.q1.a1', '84.l1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [339, 16, 340, 24, 672], 'label': '1344.2922.28.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205377
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '14.c1.a1'], 'contains': ['56.b1.a1', '56.o1.a1', '56.r1.a1', '84.m1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [25, 16, 10, 1012, 672], 'label': '1344.2922.28.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '28.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205378
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '14.b1.a1'], 'contains': ['56.c1.a1', '56.l1.a1', '56.m1.a1', '56.m1.b1', '56.q1.a1', '56.v1.a1', '56.v1.b1', '84.n1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 16, 340, 24, 672], 'label': '1344.2922.28.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205379
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '14.d1.a1'], 'contains': ['56.n1.a1', '56.p1.a1', '56.u1.a1', '84.o1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 672, 24, 16, 336], 'label': '1344.2922.28.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205380
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '14.c1.a1'], 'contains': ['56.c1.a1', '56.o1.a1', '56.r1.a1', '84.p1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [361, 16, 10, 340, 672], 'label': '1344.2922.28.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '28.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205381
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '28.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '14.d1.a1'], 'contains': ['56.p1.a1', '56.s1.a1', '56.u1.a1', '84.q1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 672, 1036, 16, 336], 'label': '1344.2922.28.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205382
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.u1.a1', '12.c1.a1', '28.c1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 16, 192, 340, 336], 'label': '1344.2922.4.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205383
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.i1.b1'], 'contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672, 192, 16], 'label': '1344.2922.32.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.a1', '16.b1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205384
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.j1.a1', '16.j1.a2', '16.k1.a1'], 'contains': ['64.a1.a1', '96.b1.a1', '224.b1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [676, 192, 16], 'label': '1344.2922.32.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205385
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '224.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [339, 16, 192], 'label': '1344.2922.32.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '32.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205386
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1'], 'contains': ['64.a1.a1', '96.d1.a1', '224.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [24, 192, 16], 'label': '1344.2922.32.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '32.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205387
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.j1.a1', '16.j1.a2'], 'contains': ['64.a1.a1', '96.e1.a1', '224.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25, 192, 16], 'label': '1344.2922.32.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205388
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.b1.b1', '84.c1.a1', '84.d1.a1', '84.h1.a1', '84.j1.a1', '84.k1.a1', '84.l1.a1', '84.n1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [3, 340, 24, 336], 'label': '1344.2922.42.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205389
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.f1.a1', '84.i1.a1', '84.m1.a1', '84.p1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [25, 10, 336], 'label': '1344.2922.42.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205390
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.c1.a1', '84.g1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 2], 'label': '1344.2922.42.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '42.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205391
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.d1.a1', '84.f1.a1', '84.o1.a1', '84.q1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 340, 24], 'label': '1344.2922.42.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205392
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.d1.a1', '84.g1.a1', '84.i1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2, 24], 'label': '1344.2922.42.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205393
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.s1.a1', '12.i1.a1', '28.i1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [10, 192, 340, 672, 336, 16], 'label': '1344.2922.4.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205394
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '14.f1.a1', '21.a1.a1'], 'contains': ['84.e1.a1', '84.e1.b1', '84.f1.a1', '84.g1.a1', '84.h1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [25, 2, 336], 'label': '1344.2922.42.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205395
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '42.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '14.g1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.h1.a1', '84.i1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 10], 'label': '1344.2922.42.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205396
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.h1.b1'], 'contains': ['96.a1.a1', '96.b1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [676, 192, 672], 'label': '1344.2922.48.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205418
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.d1.a1', '28.f1.a1', '28.h1.a1'], 'contains': ['112.a1.a1', '112.i1.a1', '168.f1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [11, 676, 672, 16], 'label': '1344.2922.56.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205397
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.l1.a1', '24.m1.a1', '24.o1.a1', '24.q1.a1', '24.r1.a1', '24.s1.a1'], 'contains': ['96.a1.a1', '336.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 672, 192], 'label': '1344.2922.48.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205398
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.j1.a1', '24.p1.a1', '24.t1.a1', '24.u1.a1'], 'contains': ['96.a1.a1', '336.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 672, 192], 'label': '1344.2922.48.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.c1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['96.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205399
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.d1.a1', '24.i1.a1', '24.i1.b1', '24.j1.a1', '24.k1.a1', '24.k1.b1', '24.l1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '336.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 192, 672], 'label': '1344.2922.48.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205400
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.b1.a1', '24.e1.a1', '24.i1.a1', '24.i1.b1', '24.m1.a1', '24.n1.a1', '24.n1.b1'], 'contains': ['96.a1.a1', '96.d1.a1', '336.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24, 192, 672], 'label': '1344.2922.48.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205401
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.f1.a1', '24.o1.a1', '24.p1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '336.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25, 192, 672], 'label': '1344.2922.48.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205402
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.d1.a1', '24.j1.a1', '24.n1.a1', '24.n1.b1', '24.q1.a1', '24.v1.a1', '24.v1.b1'], 'contains': ['96.a1.a1', '336.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 672, 192], 'label': '1344.2922.48.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205403
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.c1.a1', '24.e1.a1', '24.k1.a1', '24.k1.b1', '24.m1.a1', '24.v1.a1', '24.v1.b1'], 'contains': ['96.a1.a1', '336.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1036, 192, 672], 'label': '1344.2922.48.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205404
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '8.h1.a1', '8.k1.a1', '8.m1.a1', '8.o1.a1', '8.v1.a1', '12.d1.a1', '28.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 192, 24, 672, 676, 16], 'label': '1344.2922.4.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205405
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.h1.a1', '24.i1.a1', '24.k1.a1', '24.n1.a1', '24.r1.a1', '24.t1.a1', '24.v1.a1'], 'contains': ['96.a1.a1', '336.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [11, 192, 672], 'label': '1344.2922.48.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205406
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '24.h1.b1', '24.i1.b1', '24.k1.b1', '24.n1.b1', '24.r1.a1', '24.t1.a1', '24.v1.b1'], 'contains': ['96.a1.a1', '336.i1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [347, 192, 672], 'label': '1344.2922.48.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205407
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.f1.a1'], 'contains': ['96.b1.a1', '96.e1.a1', '336.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25, 192, 4], 'label': '1344.2922.48.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '48.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205408
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a2', '24.f1.a1'], 'contains': ['96.b1.a1', '96.e1.a1', '336.j1.a2'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25, 192, 676], 'label': '1344.2922.48.j1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.b1', 'old_label': '48.j1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205409
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.g1.a1'], 'contains': ['96.b1.a1', '336.k1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2, 4, 192], 'label': '1344.2922.48.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '48.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205410
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1', '28.e1.a1', '28.g1.a1', '28.h1.a1', '28.i1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.a1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 336, 16, 672], 'label': '1344.2922.56.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.a1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normal_contains': ['112.a1.a1', '112.c1.a1', '112.b1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205411
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1', '28.l1.a1', '28.m1.a1'], 'contains': ['112.b1.a1', '112.d1.a1', '168.j1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [339, 340, 672, 16], 'label': '1344.2922.56.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': ['8.c1.a1', '28.a1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205412
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '28.a1.a1', '28.n1.a1', '28.p1.a1'], 'contains': ['112.b1.a1', '112.g1.a1', '168.p1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 340, 672, 16], 'label': '1344.2922.56.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.c1.a1', 'normal_contained_in': ['8.e1.a1', '28.a1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205413
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '28.a1.a1', '28.d1.a1', '28.d1.b1'], 'contains': ['112.a1.a1', '112.d1.a1', '112.g1.a1', '168.b1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 676, 672, 16], 'label': '1344.2922.56.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '56.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205414
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '28.d1.a1', '28.d1.b1', '28.e1.a1'], 'contains': ['112.a1.a1', '112.e1.a1', '112.h1.a1', '168.c1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [676, 24, 16, 672], 'label': '1344.2922.56.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205415
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.g1.a1', '8.h1.a1', '8.k1.b1', '8.m1.b1', '8.o1.b1', '8.v1.b1', '12.d1.b1', '28.d1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [339, 192, 24, 672, 676, 16], 'label': '1344.2922.4.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205416
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '28.f1.a1', '28.f1.b1', '28.g1.a1'], 'contains': ['112.a1.a1', '112.f1.a1', '112.j1.a1', '112.j1.a2', '168.d1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [25, 676, 672, 16], 'label': '1344.2922.56.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '56.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205417
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '28.b1.a1', '28.f1.a1', '28.f1.b1'], 'contains': ['112.a1.a1', '112.k1.a1', '168.e1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2, 672, 4, 16], 'label': '1344.2922.56.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '56.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205419
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '28.d1.b1', '28.f1.b1', '28.h1.a1'], 'contains': ['112.a1.a1', '112.i1.b1', '168.f1.b1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [347, 676, 672, 16], 'label': '1344.2922.56.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205420
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '28.d1.a1', '28.j1.a1', '28.l1.a1'], 'contains': ['112.d1.a1', '112.e1.a1', '112.i1.a1', '168.g1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [339, 360, 672, 16], 'label': '1344.2922.56.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205421
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '28.d1.b1', '28.j1.a1', '28.l1.a1'], 'contains': ['112.d1.a1', '112.e1.a1', '112.i1.b1', '168.g1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [339, 24, 672, 16], 'label': '1344.2922.56.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205422
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '28.a1.a1', '28.j1.a1', '28.k1.a1'], 'contains': ['112.c1.a1', '112.d1.a1', '112.g1.a1', '168.h1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 336, 672, 16], 'label': '1344.2922.56.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '56.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205423
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '28.d1.a1', '28.k1.a1', '28.l1.a1'], 'contains': ['112.d1.a1', '112.h1.a1', '112.i1.a1', '168.i1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [339, 1036, 672, 16], 'label': '1344.2922.56.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205424
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '28.d1.b1', '28.k1.a1', '28.l1.a1'], 'contains': ['112.d1.a1', '112.h1.a1', '112.i1.b1', '168.i1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [339, 28, 672, 16], 'label': '1344.2922.56.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205425
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '28.e1.a1', '28.l1.a1', '28.n1.a1'], 'contains': ['112.b1.a1', '112.e1.a1', '112.h1.a1', '168.k1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [340, 24, 16, 672], 'label': '1344.2922.56.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205426
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.b1.a1', '8.i1.a1', '8.j1.a1', '12.f1.a1', '28.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [361, 192, 676, 672, 2, 16], 'label': '1344.2922.4.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205427
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '28.d1.a1', '28.j1.a1', '28.n1.a1'], 'contains': ['112.e1.a1', '112.g1.a1', '112.i1.a1', '168.l1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 24, 672, 16], 'label': '1344.2922.56.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205428
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '28.d1.b1', '28.j1.a1', '28.n1.a1'], 'contains': ['112.e1.a1', '112.g1.a1', '112.i1.b1', '168.l1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 360, 672, 16], 'label': '1344.2922.56.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205429
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.e1.a1', '28.j1.a1', '28.o1.a1'], 'contains': ['112.c1.a1', '112.e1.a1', '168.m1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [24, 336, 16, 672], 'label': '1344.2922.56.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205430
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '28.g1.a1', '28.m1.a1', '28.p1.a1'], 'contains': ['112.b1.a1', '112.f1.a1', '168.n1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [25, 340, 16, 672], 'label': '1344.2922.56.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205431
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '28.g1.a1', '28.o1.a1', '28.q1.a1'], 'contains': ['112.c1.a1', '112.f1.a1', '168.o1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [25, 336, 16, 672], 'label': '1344.2922.56.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205432
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '28.h1.a1', '28.l1.a1', '28.n1.a1'], 'contains': ['112.b1.a1', '112.i1.a1', '112.i1.b1', '168.q1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [11, 340, 672, 16], 'label': '1344.2922.56.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205433
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '28.i1.a1', '28.m1.a1', '28.p1.a1'], 'contains': ['112.b1.a1', '168.r1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [10, 340, 672, 16], 'label': '1344.2922.56.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205434
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '28.e1.a1', '28.k1.a1', '28.q1.a1'], 'contains': ['112.c1.a1', '112.h1.a1', '168.s1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1036, 336, 16, 672], 'label': '1344.2922.56.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205435
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '28.h1.a1', '28.j1.a1', '28.k1.a1'], 'contains': ['112.c1.a1', '112.i1.a1', '112.i1.b1', '168.t1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [11, 336, 672, 16], 'label': '1344.2922.56.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205436
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '28.c1.a1', '28.o1.a1', '28.q1.a1'], 'contains': ['112.c1.a1', '168.u1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 16, 336, 672], 'label': '1344.2922.56.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '56.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205437
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '4.h1.a1', '4.h1.b1', '4.j1.a1', '4.k1.a1', '4.l1.a1', '4.n1.a1', '6.b1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 16, 24, 336, 340, 192, 672], 'label': '1344.2922.2.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205438
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.b1.b1', '8.i1.a1', '8.j1.a1', '12.f1.b1', '28.f1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25, 192, 676, 672, 2, 16], 'label': '1344.2922.4.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205439
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '28.d1.a1', '28.k1.a1', '28.n1.a1'], 'contains': ['112.g1.a1', '112.h1.a1', '112.i1.a1', '168.v1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 28, 672, 16], 'label': '1344.2922.56.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205440
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '56.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.b1', '28.d1.b1', '28.k1.a1', '28.n1.a1'], 'contains': ['112.g1.a1', '112.h1.a1', '112.i1.b1', '168.v1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 1036, 672, 16], 'label': '1344.2922.56.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205484
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '56.d1.a1', '84.b1.a1', '84.b1.b1', '84.c1.a1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.g1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 676], 'label': '1344.2922.168.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '168.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205441
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1.a1', 'complements': ['21.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1'], 'contains': ['192.a1.a1', '448.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16, 192], 'label': '1344.2922.64.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['192.a1.a1', '448.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205442
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.c1.a1', '42.c1.a1', '42.d1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.u1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 340], 'label': '1344.2922.84.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.c1.a1', '28.c1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205443
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '28.d1.a1', '42.a1.a1'], 'contains': ['168.b1.a1', '168.c1.a1', '168.f1.a1', '168.g1.a1', '168.i1.a1', '168.l1.a1', '168.v1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 676, 24], 'label': '1344.2922.84.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205444
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '28.d1.b1', '42.a1.a1'], 'contains': ['168.b1.a1', '168.c1.a1', '168.f1.b1', '168.g1.b1', '168.i1.b1', '168.l1.b1', '168.v1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [339, 676, 24], 'label': '1344.2922.84.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205445
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '28.a1.a1', '42.a1.a1', '42.b1.a1', '42.c1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.h1.a1', '168.j1.a1', '168.p1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 340, 336], 'label': '1344.2922.84.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205446
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.e1.a1', '42.a1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.c1.a1', '168.k1.a1', '168.m1.a1', '168.s1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [340, 24, 336], 'label': '1344.2922.84.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205447
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '28.f1.a1', '42.f1.a1'], 'contains': ['168.d1.a1', '168.e1.a1', '168.f1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [361, 2], 'label': '1344.2922.84.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.f1.a1', 'old_label': '84.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205448
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '28.f1.b1', '42.f1.a1'], 'contains': ['168.d1.a1', '168.e1.a1', '168.f1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [25, 2], 'label': '1344.2922.84.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.f1.a1', 'old_label': '84.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205449
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.d1.a1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.o1.a1', '8.o1.b1', '8.t1.a1', '12.j1.a1', '28.j1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 192, 336, 672, 24, 16], 'label': '1344.2922.4.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205450
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.g1.a1', '42.b1.a1', '42.d1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.d1.a1', '168.n1.a1', '168.o1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [25, 340, 336], 'label': '1344.2922.84.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205451
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '28.b1.a1', '42.c1.a1', '42.e1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.e1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 336], 'label': '1344.2922.84.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205452
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '28.h1.a1', '42.a1.a1', '42.f1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.f1.a1', '168.f1.b1', '168.q1.a1', '168.t1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [11, 340, 336], 'label': '1344.2922.84.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205453
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '28.i1.a1', '42.b1.a1', '42.e1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.r1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [10, 336], 'label': '1344.2922.84.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205454
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '28.j1.a1', '42.a1.a1'], 'contains': ['168.g1.a1', '168.g1.b1', '168.h1.a1', '168.l1.a1', '168.l1.b1', '168.m1.a1', '168.t1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 24, 336], 'label': '1344.2922.84.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205455
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '28.k1.a1', '42.a1.a1'], 'contains': ['168.h1.a1', '168.i1.a1', '168.i1.b1', '168.s1.a1', '168.t1.a1', '168.v1.a1', '168.v1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 1036, 336], 'label': '1344.2922.84.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205456
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '28.l1.a1', '42.a1.a1'], 'contains': ['168.g1.a1', '168.g1.b1', '168.i1.a1', '168.i1.b1', '168.j1.a1', '168.k1.a1', '168.q1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [339, 340, 24], 'label': '1344.2922.84.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205457
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '28.m1.a1', '42.b1.a1'], 'contains': ['168.j1.a1', '168.n1.a1', '168.r1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [25, 10], 'label': '1344.2922.84.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '84.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205458
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '28.n1.a1', '42.a1.a1'], 'contains': ['168.k1.a1', '168.l1.a1', '168.l1.b1', '168.p1.a1', '168.q1.a1', '168.v1.a1', '168.v1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 340, 24], 'label': '1344.2922.84.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '84.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205459
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '28.o1.a1', '42.d1.a1'], 'contains': ['168.m1.a1', '168.o1.a1', '168.u1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 24], 'label': '1344.2922.84.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '84.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205460
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.f1.a1', '8.l1.a1', '8.m1.a1', '8.m1.b1', '8.t1.a1', '8.v1.a1', '8.v1.b1', '12.k1.a1', '28.k1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 192, 336, 672, 1036, 16], 'label': '1344.2922.4.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205461
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '28.p1.a1', '42.b1.a1'], 'contains': ['168.n1.a1', '168.p1.a1', '168.r1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [361, 10], 'label': '1344.2922.84.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '84.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205462
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '84.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '28.q1.a1', '42.d1.a1'], 'contains': ['168.o1.a1', '168.s1.a1', '168.u1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 1036], 'label': '1344.2922.84.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '84.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205463
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1', '48.i1.a1', '48.i1.b1'], 'contains': ['192.a1.a1', '672.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672, 192], 'label': '1344.2922.96.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1', '48.c1.a1', '48.b1.a1'], 'normal_contains': ['192.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205464
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.j1.a1', '48.j1.a2', '48.k1.a1'], 'contains': ['192.a1.a1', '672.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [676, 192], 'label': '1344.2922.96.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '96.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205465
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.d1.a1'], 'contains': ['192.a1.a1', '672.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [339, 192], 'label': '1344.2922.96.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '96.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205466
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.e1.a1'], 'contains': ['192.a1.a1', '672.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [24, 192], 'label': '1344.2922.96.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '96.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205467
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.f1.a1', '48.j1.a1', '48.j1.a2'], 'contains': ['192.a1.a1', '672.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [25, 192], 'label': '1344.2922.96.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '96.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205468
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.d1.a1', '56.e1.a1', '56.f1.a1', '56.g1.a1', '56.h1.a1', '56.h1.b1'], 'contains': ['224.a1.a1', '224.b1.a1', '336.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [676, 672, 16], 'label': '1344.2922.112.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1'], 'normal_contains': ['224.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205469
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1', '56.l1.a1', '56.o1.a1', '56.q1.a1', '56.r1.a1'], 'contains': ['224.a1.a1', '336.b1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 16, 672], 'label': '1344.2922.112.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.b1.a1', 'normal_contained_in': ['16.b1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1'], 'normal_contains': ['224.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205470
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '56.a1.a1', '56.j1.a1', '56.n1.a1', '56.p1.a1', '56.s1.a1', '56.t1.a1', '56.u1.a1'], 'contains': ['224.a1.a1', '336.c1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 16, 672], 'label': '1344.2922.112.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': ['16.c1.a1', '56.a1.a1'], 'normal_contains': ['224.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205471
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.k1.a1', '8.k1.b1', '8.m1.a1', '8.m1.b1', '8.n1.a1', '8.r1.a1', '12.l1.a1', '28.l1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [339, 192, 24, 672, 340, 16], 'label': '1344.2922.4.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205472
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '56.b1.a1', '56.d1.a1', '56.i1.a1', '56.i1.b1', '56.j1.a1', '56.k1.a1', '56.k1.b1'], 'contains': ['224.a1.a1', '224.c1.a1', '336.d1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [339, 672, 16], 'label': '1344.2922.112.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '112.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205473
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '56.e1.a1', '56.i1.a1', '56.i1.b1', '56.l1.a1', '56.m1.a1', '56.m1.b1', '56.n1.a1'], 'contains': ['224.a1.a1', '224.d1.a1', '336.e1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [24, 672, 16], 'label': '1344.2922.112.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205474
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '56.f1.a1', '56.o1.a1', '56.p1.a1'], 'contains': ['224.a1.a1', '224.e1.a1', '336.f1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [25, 672, 16], 'label': '1344.2922.112.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.g1.a1', 'old_label': '112.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205475
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '56.c1.a1', '56.d1.a1', '56.j1.a1', '56.m1.a1', '56.m1.b1', '56.v1.a1', '56.v1.b1'], 'contains': ['224.a1.a1', '336.g1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 16], 'label': '1344.2922.112.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '112.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205476
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '56.e1.a1', '56.k1.a1', '56.k1.b1', '56.l1.a1', '56.s1.a1', '56.v1.a1', '56.v1.b1'], 'contains': ['224.a1.a1', '336.h1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1036, 16, 672], 'label': '1344.2922.112.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205477
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '56.h1.a1', '56.i1.a1', '56.k1.a1', '56.m1.a1', '56.q1.a1', '56.t1.a1', '56.v1.a1'], 'contains': ['224.a1.a1', '336.i1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [11, 672, 16], 'label': '1344.2922.112.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205478
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '56.h1.b1', '56.i1.b1', '56.k1.b1', '56.m1.b1', '56.q1.a1', '56.t1.a1', '56.v1.b1'], 'contains': ['224.a1.a1', '336.i1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [347, 672, 16], 'label': '1344.2922.112.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205479
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '56.f1.a1'], 'contains': ['224.b1.a1', '224.e1.a1', '336.j1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [25, 4, 16], 'label': '1344.2922.112.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.f1.a1', 'old_label': '112.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205480
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a2', '56.f1.a1'], 'contains': ['224.b1.a1', '224.e1.a1', '336.j1.a2'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [25, 676, 16], 'label': '1344.2922.112.j1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.f1.b1', 'old_label': '112.j1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.j1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205481
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '112.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '56.g1.a1'], 'contains': ['224.b1.a1', '336.k1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2, 4, 16], 'label': '1344.2922.112.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '112.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205482
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.p1.a1', '8.s1.a1', '12.m1.a1', '28.m1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25, 192, 1012, 672, 10, 16], 'label': '1344.2922.4.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205483
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1', '84.c1.a1', '84.d1.a1', '84.f1.a1', '84.g1.a1', '84.h1.a1', '84.i1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 336], 'label': '1344.2922.168.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.a1.a1', '56.a1.a1', '84.a1.a1'], 'normal_contains': ['336.a1.a1', '336.c1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205485
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '56.e1.a1', '84.b1.a1', '84.b1.b1', '84.d1.a1'], 'contains': ['336.a1.a1', '336.e1.a1', '336.h1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [676, 24], 'label': '1344.2922.168.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205486
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '56.f1.a1', '84.e1.a1', '84.e1.b1', '84.f1.a1'], 'contains': ['336.a1.a1', '336.f1.a1', '336.j1.a1', '336.j1.a2'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [25, 676, 672], 'label': '1344.2922.168.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '168.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205487
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '56.g1.a1', '84.e1.a1', '84.e1.b1', '84.g1.a1'], 'contains': ['336.a1.a1', '336.k1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 672], 'label': '1344.2922.168.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '168.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205488
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '56.h1.a1', '84.b1.a1', '84.e1.a1', '84.h1.a1'], 'contains': ['336.a1.a1', '336.i1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [11, 676], 'label': '1344.2922.168.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205489
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '56.h1.b1', '84.b1.b1', '84.e1.b1', '84.h1.a1'], 'contains': ['336.a1.a1', '336.i1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [347, 676], 'label': '1344.2922.168.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205490
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '56.i1.a1', '84.b1.a1', '84.j1.a1', '84.l1.a1'], 'contains': ['336.d1.a1', '336.e1.a1', '336.i1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [339, 360], 'label': '1344.2922.168.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205491
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.v1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '56.i1.b1', '84.b1.b1', '84.j1.a1', '84.l1.a1'], 'contains': ['336.d1.a1', '336.e1.a1', '336.i1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [339, 24], 'label': '1344.2922.168.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205492
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '56.j1.a1', '84.c1.a1', '84.j1.a1', '84.k1.a1'], 'contains': ['336.c1.a1', '336.d1.a1', '336.g1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 336], 'label': '1344.2922.168.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '168.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205493
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.e1.a1', '8.n1.a1', '8.o1.a1', '8.o1.b1', '8.r1.a1', '8.v1.a1', '8.v1.b1', '12.n1.a1', '28.n1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 192, 24, 672, 340, 16], 'label': '1344.2922.4.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205494
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '56.k1.a1', '84.b1.a1', '84.k1.a1', '84.l1.a1'], 'contains': ['336.d1.a1', '336.h1.a1', '336.i1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [339, 1036], 'label': '1344.2922.168.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205495
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '56.k1.b1', '84.b1.b1', '84.k1.a1', '84.l1.a1'], 'contains': ['336.d1.a1', '336.h1.a1', '336.i1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [339, 28], 'label': '1344.2922.168.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205496
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '56.b1.a1', '84.c1.a1', '84.l1.a1', '84.m1.a1'], 'contains': ['336.b1.a1', '336.d1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [339, 340], 'label': '1344.2922.168.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205497
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '56.l1.a1', '84.d1.a1', '84.l1.a1', '84.n1.a1'], 'contains': ['336.b1.a1', '336.e1.a1', '336.h1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [340, 24], 'label': '1344.2922.168.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205498
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '56.m1.a1', '84.b1.a1', '84.j1.a1', '84.n1.a1'], 'contains': ['336.e1.a1', '336.g1.a1', '336.i1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 24], 'label': '1344.2922.168.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205499
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.b1', '56.m1.b1', '84.b1.b1', '84.j1.a1', '84.n1.a1'], 'contains': ['336.e1.a1', '336.g1.a1', '336.i1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 360], 'label': '1344.2922.168.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205500
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.n1.a1', '84.d1.a1', '84.j1.a1', '84.o1.a1'], 'contains': ['336.c1.a1', '336.e1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [24, 336], 'label': '1344.2922.168.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205501
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '56.o1.a1', '84.f1.a1', '84.m1.a1', '84.p1.a1'], 'contains': ['336.b1.a1', '336.f1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [25, 340], 'label': '1344.2922.168.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '168.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205502
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '56.p1.a1', '84.f1.a1', '84.o1.a1', '84.q1.a1'], 'contains': ['336.c1.a1', '336.f1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [25, 336], 'label': '1344.2922.168.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '168.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205503
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '56.c1.a1', '84.c1.a1', '84.n1.a1', '84.p1.a1'], 'contains': ['336.b1.a1', '336.g1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 340], 'label': '1344.2922.168.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205504
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.d1.a1', '8.q1.a1', '8.u1.a1', '12.o1.a1', '28.o1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 16, 336, 24, 672], 'label': '1344.2922.4.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205505
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '56.q1.a1', '84.h1.a1', '84.l1.a1', '84.n1.a1'], 'contains': ['336.b1.a1', '336.i1.a1', '336.i1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [11, 340], 'label': '1344.2922.168.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205506
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '56.r1.a1', '84.i1.a1', '84.m1.a1', '84.p1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [10], 'label': '1344.2922.168.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205507
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.s1.a1', '84.d1.a1', '84.k1.a1', '84.q1.a1'], 'contains': ['336.c1.a1', '336.h1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1036, 336], 'label': '1344.2922.168.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205508
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '56.t1.a1', '84.h1.a1', '84.j1.a1', '84.k1.a1'], 'contains': ['336.c1.a1', '336.i1.a1', '336.i1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [11, 336], 'label': '1344.2922.168.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205509
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '56.u1.a1', '84.a1.a1', '84.o1.a1', '84.q1.a1'], 'contains': ['336.c1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1], 'label': '1344.2922.168.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '168.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205510
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '56.v1.a1', '84.b1.a1', '84.k1.a1', '84.n1.a1'], 'contains': ['336.g1.a1', '336.h1.a1', '336.i1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 28], 'label': '1344.2922.168.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205511
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '168.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.b1', '56.v1.b1', '84.b1.b1', '84.k1.a1', '84.n1.a1'], 'contains': ['336.g1.a1', '336.h1.a1', '336.i1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 1036], 'label': '1344.2922.168.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205512
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1', '96.e1.a1'], 'contains': ['1344.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [192], 'label': '1344.2922.192.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205513
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1', '112.d1.a1', '112.e1.a1', '112.f1.a1', '112.g1.a1', '112.h1.a1', '112.i1.a1', '112.i1.b1'], 'contains': ['448.a1.a1', '672.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672, 16], 'label': '1344.2922.224.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.a1.a1', 'normal_contained_in': ['32.a1.a1', '112.a1.a1', '112.c1.a1', '112.b1.a1'], 'normal_contains': ['448.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205514
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '224.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '112.a1.a1', '112.j1.a1', '112.j1.a2', '112.k1.a1'], 'contains': ['448.a1.a1', '672.b1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [676, 16], 'label': '1344.2922.224.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '224.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205515
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '8.p1.a1', '8.s1.a1', '12.p1.a1', '28.p1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [361, 192, 340, 672, 10, 16], 'label': '1344.2922.4.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205516
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '224.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '112.d1.a1'], 'contains': ['448.a1.a1', '672.c1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [339, 16], 'label': '1344.2922.224.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '224.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205517
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '112.e1.a1'], 'contains': ['448.a1.a1', '672.d1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [24, 16], 'label': '1344.2922.224.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.n1.a1', 'old_label': '224.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205518
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '112.f1.a1', '112.j1.a1', '112.j1.a2'], 'contains': ['448.a1.a1', '672.e1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [25, 16], 'label': '1344.2922.224.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.f1.a1', 'old_label': '224.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205519
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.b1.a1', '168.c1.a1', '168.d1.a1', '168.e1.a1', '168.f1.a1', '168.f1.b1'], 'contains': ['672.a1.a1', '672.b1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [676, 672], 'label': '1344.2922.336.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205520
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '112.b1.a1', '168.a1.a1', '168.j1.a1', '168.k1.a1', '168.n1.a1', '168.p1.a1', '168.q1.a1', '168.r1.a1'], 'contains': ['672.a1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340], 'label': '1344.2922.336.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.b1.a1', 'normal_contained_in': ['48.b1.a1', '112.b1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205521
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '112.c1.a1', '168.a1.a1', '168.h1.a1', '168.m1.a1', '168.o1.a1', '168.s1.a1', '168.t1.a1', '168.u1.a1'], 'contains': ['672.a1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336], 'label': '1344.2922.336.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.c1.a1', 'normal_contained_in': ['48.c1.a1', '112.c1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205522
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '112.d1.a1', '168.b1.a1', '168.g1.a1', '168.g1.b1', '168.h1.a1', '168.i1.a1', '168.i1.b1', '168.j1.a1'], 'contains': ['672.a1.a1', '672.c1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 672], 'label': '1344.2922.336.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '336.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205523
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '112.e1.a1', '168.c1.a1', '168.g1.a1', '168.g1.b1', '168.k1.a1', '168.l1.a1', '168.l1.b1', '168.m1.a1'], 'contains': ['672.a1.a1', '672.d1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [24, 672], 'label': '1344.2922.336.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205524
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '112.f1.a1', '168.d1.a1', '168.n1.a1', '168.o1.a1'], 'contains': ['672.a1.a1', '672.e1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [25, 672], 'label': '1344.2922.336.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.g1.a1', 'old_label': '336.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205525
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '112.g1.a1', '168.b1.a1', '168.h1.a1', '168.l1.a1', '168.l1.b1', '168.p1.a1', '168.v1.a1', '168.v1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3], 'label': '1344.2922.336.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '336.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205526
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.f1.a1', '8.q1.a1', '8.u1.a1', '12.q1.a1', '28.q1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 16, 336, 1036, 672], 'label': '1344.2922.4.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205527
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '112.h1.a1', '168.c1.a1', '168.i1.a1', '168.i1.b1', '168.k1.a1', '168.s1.a1', '168.v1.a1', '168.v1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1036], 'label': '1344.2922.336.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205528
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '112.i1.a1', '168.f1.a1', '168.g1.a1', '168.i1.a1', '168.l1.a1', '168.q1.a1', '168.t1.a1', '168.v1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [11], 'label': '1344.2922.336.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '336.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205529
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '112.i1.b1', '168.f1.b1', '168.g1.b1', '168.i1.b1', '168.l1.b1', '168.q1.a1', '168.t1.a1', '168.v1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [347], 'label': '1344.2922.336.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '336.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205530
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '112.j1.a1', '168.d1.a1'], 'contains': ['672.b1.a1', '672.e1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [25, 4], 'label': '1344.2922.336.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.f1.a1', 'old_label': '336.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205531
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a2', '112.j1.a2', '168.d1.a1'], 'contains': ['672.b1.a1', '672.e1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [25, 676], 'label': '1344.2922.336.j1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.f1.b1', 'old_label': '336.j1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205532
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '112.k1.a1', '168.e1.a1'], 'contains': ['672.b1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2], 'label': '1344.2922.336.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '336.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205533
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '448.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.d1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '224.a1.a1', '224.b1.a1', '224.c1.a1', '224.d1.a1', '224.e1.a1'], 'contains': ['1344.a1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16], 'label': '1344.2922.448.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '448.a1.a1', 'normal_contained_in': ['64.a1.a1', '224.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '448.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205534
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1', '336.d1.a1', '336.e1.a1', '336.f1.a1', '336.g1.a1', '336.h1.a1', '336.i1.a1', '336.i1.b1'], 'contains': ['1344.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672], 'label': '1344.2922.672.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '672.a1.a1', 'normal_contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.c1.a1', '336.b1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205535
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '672.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '224.b1.a1', '336.a1.a1', '336.j1.a1', '336.j1.a2', '336.k1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [676], 'label': '1344.2922.672.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '672.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205536
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '672.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '224.c1.a1', '336.d1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [339], 'label': '1344.2922.672.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '672.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205537
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['224.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.o1.a1', '12.q1.a1', '42.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 24, 336, 340, 672], 'label': '1344.2922.6.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205538
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '224.d1.a1', '336.e1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [24], 'label': '1344.2922.672.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.n1.a1', 'old_label': '672.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205539
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '224.e1.a1', '336.f1.a1', '336.j1.a1', '336.j1.a2'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': None, 'generators': [25], 'label': '1344.2922.672.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.f1.a1', 'old_label': '672.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205540
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '1344.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '448.a1.a1', '672.a1.a1', '672.b1.a1', '672.c1.a1', '672.d1.a1', '672.e1.a1'], 'contains': [], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '1344.2922.1344.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1344.a1.a1', 'normal_contained_in': ['192.a1.a1', '448.a1.a1', '672.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1344.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205541
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.g1.a1', '4.m1.a1', '4.p1.a1', '6.c1.a1', '14.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25, 16, 336, 1012, 10, 192, 672], 'label': '1344.2922.2.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205542
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1', '12.h1.a1', '12.j1.a1', '12.k1.a1', '12.l1.a1', '12.n1.a1', '42.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 192, 24, 336, 340, 672], 'label': '1344.2922.6.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205543
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.i1.a1', '12.m1.a1', '12.p1.a1', '42.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25, 192, 336, 1012, 10, 672], 'label': '1344.2922.6.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205544
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.e1.a1', '12.g1.a1', '42.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 672, 192, 340, 2, 336], 'label': '1344.2922.6.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205545
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.i1.a1', '42.e1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 4, 1008, 24, 672], 'label': '1344.2922.6.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205546
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.f1.a1', '12.f1.b1', '12.g1.a1', '12.h1.a1', '42.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [25, 192, 336, 676, 2, 672], 'label': '1344.2922.6.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205547
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.h1.a1', '12.i1.a1', '42.g1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 676, 336, 10, 672], 'label': '1344.2922.6.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205548
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.c1.a1', '14.d1.a1', '14.e1.a1', '14.f1.a1', '14.g1.a1', '21.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 336, 2, 16, 24, 340], 'label': '1344.2922.7.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205549
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1', '56.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 16, 192, 336, 672], 'label': '1344.2922.8.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.b1.a1', '24.a1.a1', '56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205550
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.i1.a1', '24.h1.a1', '56.h1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [11, 672, 16, 676, 192], 'label': '1344.2922.8.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205551
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.h1.b1', '4.i1.b1'], 'contains': ['16.a1.a1', '16.i1.b1', '24.h1.b1', '56.h1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [347, 672, 16, 676, 192], 'label': '1344.2922.8.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205552
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': ['672.d1.a1', '672.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.f1.a1', '6.d1.a1', '14.a1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 192, 340, 2, 16, 336], 'label': '1344.2922.2.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.f1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205553
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '24.l1.a1', '56.b1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [339, 192, 672, 340, 16], 'label': '1344.2922.8.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1', '56.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205554
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.o1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '24.b1.a1', '56.n1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24, 16, 672, 336, 192], 'label': '1344.2922.8.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.c1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205555
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.n1.a1', '4.p1.a1'], 'contains': ['16.b1.a1', '16.g1.a1', '24.q1.a1', '56.c1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 192, 672, 340, 16], 'label': '1344.2922.8.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1', '56.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205556
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.k1.a1', '4.q1.a1'], 'contains': ['16.c1.a1', '16.h1.a1', '24.c1.a1', '56.s1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1036, 16, 672, 336, 192], 'label': '1344.2922.8.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.c1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205557
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.g1.a1', '24.d1.a1', '56.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 192, 672, 676, 16], 'label': '1344.2922.8.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205558
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.h1.a1', '24.e1.a1', '56.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [676, 16, 672, 24, 192], 'label': '1344.2922.8.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205559
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.j1.a1', '16.j1.a2', '24.f1.a1', '56.f1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25, 672, 16, 676, 192], 'label': '1344.2922.8.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205560
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '16.k1.a1', '24.g1.a1', '56.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2, 192, 4, 672, 16], 'label': '1344.2922.8.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205561
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.j1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.i1.a1', '24.i1.a1', '56.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [339, 672, 16, 360, 192], 'label': '1344.2922.8.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205562
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.j1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.i1.b1', '24.i1.b1', '56.i1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [339, 672, 16, 24, 192], 'label': '1344.2922.8.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205563
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '4.o1.a1', '4.q1.a1', '6.a1.a1', '14.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 24, 16, 340, 192, 336], 'label': '1344.2922.2.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205564
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.g1.a1', '24.j1.a1', '56.j1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 192, 672, 336, 16], 'label': '1344.2922.8.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205565
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.k1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.h1.a1', '16.i1.a1', '24.k1.a1', '56.k1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [339, 672, 16, 1036, 192], 'label': '1344.2922.8.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205566
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.k1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.h1.a1', '16.i1.b1', '24.k1.b1', '56.k1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [339, 672, 16, 28, 192], 'label': '1344.2922.8.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205567
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.h1.a1', '24.m1.a1', '56.l1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [340, 16, 672, 24, 192], 'label': '1344.2922.8.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205568
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.j1.a1', '4.n1.a1'], 'contains': ['16.e1.a1', '16.g1.a1', '16.i1.a1', '24.n1.a1', '56.m1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 16, 24, 192], 'label': '1344.2922.8.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205569
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.j1.a1', '4.n1.a1'], 'contains': ['16.e1.a1', '16.g1.a1', '16.i1.b1', '24.n1.b1', '56.m1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 16, 360, 192], 'label': '1344.2922.8.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205570
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.m1.a1', '4.p1.a1'], 'contains': ['16.b1.a1', '16.f1.a1', '24.o1.a1', '56.o1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25, 16, 672, 340, 192], 'label': '1344.2922.8.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205571
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.o1.a1', '4.q1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '24.p1.a1', '56.p1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [25, 16, 672, 336, 192], 'label': '1344.2922.8.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205572
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.i1.b1', '24.r1.a1', '56.q1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [11, 672, 16, 340, 192], 'label': '1344.2922.8.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205573
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.m1.a1', '4.p1.a1'], 'contains': ['16.b1.a1', '24.s1.a1', '56.r1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [10, 672, 16, 340, 192], 'label': '1344.2922.8.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205574
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': ['672.e1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1', '6.e1.a1', '14.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 16, 4, 1008, 24, 192, 672], 'label': '1344.2922.2.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205575
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.c1.a1', '16.i1.a1', '16.i1.b1', '24.t1.a1', '56.t1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [11, 672, 16, 336, 192], 'label': '1344.2922.8.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205576
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.o1.a1', '4.q1.a1'], 'contains': ['16.c1.a1', '24.u1.a1', '56.u1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 336, 16, 672], 'label': '1344.2922.8.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205577
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.k1.a1', '4.n1.a1'], 'contains': ['16.g1.a1', '16.h1.a1', '16.i1.a1', '24.v1.a1', '56.v1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 16, 28, 192], 'label': '1344.2922.8.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205578
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.k1.a1', '4.n1.a1'], 'contains': ['16.g1.a1', '16.h1.a1', '16.i1.b1', '24.v1.b1', '56.v1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 16, 1036, 192], 'label': '1344.2922.8.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205579
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '24.e1.a1', '24.m1.a1', '84.d1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 336, 672, 24, 192], 'label': '1344.2922.12.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205580
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.o1.a1', '24.p1.a1', '84.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25, 336, 672, 340, 192], 'label': '1344.2922.12.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205581
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.u1.a1', '84.a1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 340, 672], 'label': '1344.2922.12.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205582
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.h1.a1', '24.i1.a1', '24.k1.a1', '24.n1.a1', '24.v1.a1', '84.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 24, 672, 676, 192], 'label': '1344.2922.12.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205583
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.b1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.h1.b1', '24.i1.b1', '24.k1.b1', '24.n1.b1', '24.v1.b1', '84.b1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 24, 672, 676, 192], 'label': '1344.2922.12.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205584
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.j1.a1', '24.l1.a1', '24.q1.a1', '84.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 336, 192, 340, 672], 'label': '1344.2922.12.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205585
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '2.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': ['672.d1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '6.f1.a1', '14.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [25, 16, 336, 676, 2, 192, 672], 'label': '1344.2922.2.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205586
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.f1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.h1.a1', '84.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [361, 676, 672, 2, 192], 'label': '1344.2922.12.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205587
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.f1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.h1.b1', '84.e1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25, 676, 672, 2, 192], 'label': '1344.2922.12.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205588
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.g1.a1', '84.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 4, 336, 672], 'label': '1344.2922.12.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205589
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '24.h1.b1', '24.r1.a1', '24.t1.a1', '84.h1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [11, 336, 672, 340, 192], 'label': '1344.2922.12.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205590
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.c1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.s1.a1', '84.i1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [10, 340, 672, 336, 192], 'label': '1344.2922.12.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205591
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.i1.a1', '24.i1.b1', '24.j1.a1', '24.n1.a1', '24.n1.b1', '24.t1.a1', '84.j1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 336, 672, 24, 192], 'label': '1344.2922.12.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205592
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.b1.a1'], 'contains': ['24.c1.a1', '24.j1.a1', '24.k1.a1', '24.k1.b1', '24.t1.a1', '24.v1.a1', '24.v1.b1', '84.k1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 336, 672, 1036, 192], 'label': '1344.2922.12.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205593
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.b1.a1'], 'contains': ['24.i1.a1', '24.i1.b1', '24.k1.a1', '24.k1.b1', '24.l1.a1', '24.m1.a1', '24.r1.a1', '84.l1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 24, 672, 340, 192], 'label': '1344.2922.12.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205594
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.c1.a1'], 'contains': ['24.l1.a1', '24.o1.a1', '24.s1.a1', '84.m1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [25, 1012, 672, 10, 192], 'label': '1344.2922.12.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205595
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.b1.a1'], 'contains': ['24.m1.a1', '24.n1.a1', '24.n1.b1', '24.q1.a1', '24.r1.a1', '24.v1.a1', '24.v1.b1', '84.n1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 24, 672, 340, 192], 'label': '1344.2922.12.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205596
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '2.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.d1.a1', '672.e1.a1', '672.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.f1.a1', '4.g1.a1', '6.g1.a1', '14.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 16, 676, 336, 10, 192, 672], 'label': '1344.2922.2.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205597
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.p1.a1', '24.u1.a1', '84.o1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 336, 672, 24, 192], 'label': '1344.2922.12.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205598
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.c1.a1'], 'contains': ['24.o1.a1', '24.q1.a1', '24.s1.a1', '84.p1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [361, 340, 672, 10, 192], 'label': '1344.2922.12.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205599
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.p1.a1', '24.u1.a1', '84.q1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 336, 672, 1036, 192], 'label': '1344.2922.12.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205600
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': ['96.d1.a1', '96.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '42.c1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 16, 672, 2, 340, 336], 'label': '1344.2922.14.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205601
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.d1.a1', '28.d1.b1', '28.e1.a1', '28.h1.a1', '28.j1.a1', '28.k1.a1', '28.l1.a1', '28.n1.a1', '42.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 16, 672, 340, 24, 336], 'label': '1344.2922.14.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205602
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.g1.a1', '28.i1.a1', '28.m1.a1', '28.p1.a1', '42.b1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [25, 16, 672, 10, 336, 1012], 'label': '1344.2922.14.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205603
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.e1.a1', '28.g1.a1', '28.o1.a1', '28.q1.a1', '42.d1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 336, 340, 24, 16], 'label': '1344.2922.14.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205604
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.e1.a1', '28.i1.a1', '42.e1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2, 16, 672, 24, 4, 1008], 'label': '1344.2922.14.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205605
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '14.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.f1.a1', '28.f1.b1', '28.g1.a1', '28.h1.a1', '42.f1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [25, 16, 672, 2, 336, 676], 'label': '1344.2922.14.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205606
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '14.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.h1.a1', '28.i1.a1', '42.g1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 16, 672, 10, 676, 336], 'label': '1344.2922.14.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205607
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '21.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 672, 24, 340, 2, 192, 336], 'label': '1344.2922.3.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205608
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '48.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [676, 16, 192, 672], 'label': '1344.2922.16.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205609
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.c1.a1', '8.e1.a1', '8.n1.a1', '8.p1.a1', '8.r1.a1', '8.s1.a1'], 'contains': ['32.a1.a1', '48.b1.a1', '112.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [340, 192, 672, 16], 'label': '1344.2922.16.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.e1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1', '112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205610
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.f1.a1', '8.l1.a1', '8.q1.a1', '8.t1.a1', '8.u1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '112.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 192, 672, 16], 'label': '1344.2922.16.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.d1.a1', '8.f1.a1'], 'normal_contains': ['32.a1.a1', '48.c1.a1', '112.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205611
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.g1.a1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.m1.a1', '8.m1.b1'], 'contains': ['32.a1.a1', '32.c1.a1', '48.d1.a1', '112.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [339, 192, 16, 672], 'label': '1344.2922.16.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205612
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.h1.a1', '8.k1.a1', '8.k1.b1', '8.n1.a1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '32.d1.a1', '48.e1.a1', '112.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24, 16, 192, 672], 'label': '1344.2922.16.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205613
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.p1.a1', '8.q1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '48.f1.a1', '112.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [25, 16, 192, 672], 'label': '1344.2922.16.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205614
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.g1.a1', '8.l1.a1', '8.o1.a1', '8.o1.b1', '8.v1.a1', '8.v1.b1'], 'contains': ['32.a1.a1', '48.g1.a1', '112.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 16, 192], 'label': '1344.2922.16.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205615
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.h1.a1', '8.m1.a1', '8.m1.b1', '8.n1.a1', '8.v1.a1', '8.v1.b1'], 'contains': ['32.a1.a1', '48.h1.a1', '112.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1036, 672, 192, 16], 'label': '1344.2922.16.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205616
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.k1.a1', '8.m1.a1', '8.o1.a1', '8.r1.a1', '8.t1.a1', '8.v1.a1'], 'contains': ['32.a1.a1', '48.i1.a1', '112.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [11, 16, 192, 672], 'label': '1344.2922.16.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 72205617
    {'ambient': '1344.2922', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.k1.b1', '8.m1.b1', '8.o1.b1', '8.r1.a1', '8.t1.a1', '8.v1.b1'], 'contains': ['32.a1.a1', '48.i1.b1', '112.i1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [347, 16, 192, 672], 'label': '1344.2922.16.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}