Abstract group data - 1344.8544

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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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [12, 12, 6, 12, 84, 12, 84, 12], 'aut_gens': [[1, 2, 4, 8], [1, 1122, 788, 1193], [1, 1122, 500, 105], [673, 898, 1284, 536], [1, 674, 532, 537], [1, 226, 1140, 345], [1, 226, 996, 473], [1, 226, 1188, 681], [1, 898, 180, 1193]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 42, 'aut_perms': [201502955086442501489525606650096298672720301175290, 442911044142796437683287636230314615118185028638442, 337101016291933557611705784450351546560503588839579, 468328903350169109977187049528835615891433868030664, 220117737012561018722410665452674101424172790724265, 1306172338805385348449560672657638014200123404803878, 391462449947708603298862550897409145716533530262228, 611303883652543997239625930298230478794882833663459], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 2, 1], [2, 6, 1, 1], [2, 28, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 1, 2], [4, 28, 1, 1], [4, 28, 2, 1], [4, 84, 1, 1], [4, 84, 2, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 56, 1, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 12, 2, 1], [12, 4, 1, 2], [12, 56, 1, 1], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 6, 6, 1], [14, 12, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [28, 2, 6, 1], [28, 4, 3, 1], [28, 6, 6, 1], [28, 12, 3, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 4, 12, 1], [56, 12, 12, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{21}.(C_6\\times D_4).C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 5451351369529179689, 'autcentquo_nilpotent': False, 'autcentquo_order': 2016, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 3, 2], [2, 6, 1], [2, 28, 1], [2, 84, 1], [3, 2, 1], [4, 2, 2], [4, 6, 2], [4, 28, 3], [4, 84, 3], [6, 2, 1], [6, 4, 1], [6, 56, 1], [7, 2, 3], [8, 4, 2], [8, 12, 2], [12, 4, 2], [12, 56, 3], [14, 2, 3], [14, 4, 3], [14, 6, 6], [14, 12, 3], [21, 4, 3], [24, 8, 2], [28, 2, 6], [28, 4, 3], [28, 6, 6], [28, 12, 3], [42, 4, 3], [42, 8, 3], [56, 4, 12], [56, 12, 12], [84, 4, 6], [84, 8, 3], [168, 8, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '672.1141', 'commutator_count': 1, 'commutator_label': '84.6', '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': 8544, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['224.104', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 28, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 1, 2], [4, 28, 1, 3], [4, 84, 1, 3], [6, 2, 1, 1], [6, 4, 1, 1], [6, 56, 1, 1], [7, 2, 3, 1], [8, 4, 1, 2], [8, 12, 1, 2], [12, 4, 1, 2], [12, 56, 1, 3], [14, 2, 3, 1], [14, 4, 3, 1], [14, 6, 3, 2], [14, 12, 3, 1], [21, 4, 3, 1], [24, 8, 1, 2], [28, 2, 6, 1], [28, 4, 3, 1], [28, 6, 6, 1], [28, 12, 3, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 4, 6, 2], [56, 12, 6, 2], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 29877120, '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': '4.1', 'frattini_quotient': '336.219', 'hash': 8544, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 2, 84], 'inner_gens': [[1, 2, 4, 680], [1, 2, 4, 904], [1, 2, 4, 664], [673, 450, 692, 8]], 'inner_hash': 1141, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_6\\times D_{28}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 96, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 60], [4, 40], [8, 7]], 'label': '1344.8544', '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': 'C168.C2^3', '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': 43, 'number_characteristic_subgroups': 78, 'number_conjugacy_classes': 123, 'number_divisions': 54, 'number_normal_subgroups': 140, 'number_subgroup_autclasses': 400, 'number_subgroup_classes': 516, 'number_subgroups': 4468, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 127], [3, 2], [4, 352], [6, 62], [7, 6], [8, 32], [12, 176], [14, 90], [21, 12], [24, 16], [28, 96], [42, 36], [56, 192], [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, 0, 1], 'outer_gens': [[673, 2, 4, 8], [1, 674, 4, 8], [1, 2, 4, 344], [1, 2, 4, 921]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [40320, 3628800, 24, 723], '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, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 4], [6, 8], [8, 1], [12, 8], [24, 4], [48, 1]], 'representations': {'PC': {'code': 18140945576534334090138194475257871732853564089092065147689227, 'gens': [1, 2, 3, 4], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -7, 5376, 21763, 14475, 5331, 91, 9292, 13300, 116, 22285, 15765, 141, 14350, 17942, 222, 18455]}, 'Perm': {'d': 26, 'gens': [621574835364361536753643, 355687428096000, 3079988947639, 4491426195058, 5670545596524, 7177921676593, 6758061133824000, 16754357281155028254720000]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{168}.C_2^3', '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: 116985798
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 8544, 'group_order': 1344, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 116985833
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 8544, 'group_order': 1344, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 672, 'size': 1}
  • id: 116985844
    {'aut_label': '2B', 'centralizer': '2.b1.a1', 'counter': 3, 'group_counter': 8544, 'group_order': 1344, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 337, 'size': 2}
  • id: 116985855
    {'aut_label': '2C', 'centralizer': '3.a1.a1', 'counter': 4, 'group_counter': 8544, 'group_order': 1344, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 2, 'size': 3}
  • id: 116985866
    {'aut_label': '2C', 'centralizer': '3.a1.a1', 'counter': 5, 'group_counter': 8544, 'group_order': 1344, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 226, 'size': 3}
  • id: 116985877
    {'aut_label': '2E', 'centralizer': '6.c1.a1', 'counter': 6, 'group_counter': 8544, 'group_order': 1344, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 787, 'size': 6}
  • id: 116985888
    {'aut_label': '2F', 'centralizer': '28.n1.a1', 'counter': 7, 'group_counter': 8544, 'group_order': 1344, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 54, 'size': 28}
  • id: 116985899
    {'aut_label': '2G', 'centralizer': '84.l1.a1', 'counter': 8, 'group_counter': 8544, 'group_order': 1344, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 84, 'size': 84}
  • id: 116985910
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 9, 'group_counter': 8544, 'group_order': 1344, 'label': '3A', 'order': 3, 'powers': [9, 1, 9], 'representative': 896, 'size': 2}
  • id: 116985799
    {'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 10, 'group_counter': 8544, 'group_order': 1344, 'label': '4A', 'order': 4, 'powers': [2, 10, 10], 'representative': 1008, 'size': 2}
  • id: 116985810
    {'aut_label': '4B', 'centralizer': '2.a1.a1', 'counter': 11, 'group_counter': 8544, 'group_order': 1344, 'label': '4B', 'order': 4, 'powers': [2, 11, 11], 'representative': 1, 'size': 2}
  • id: 116985821
    {'aut_label': '4C', 'centralizer': '6.d1.a1', 'counter': 12, 'group_counter': 8544, 'group_order': 1344, 'label': '4C', 'order': 4, 'powers': [2, 12, 12], 'representative': 114, 'size': 6}
  • id: 116985826
    {'aut_label': '4D', 'centralizer': '6.b1.a1', 'counter': 13, 'group_counter': 8544, 'group_order': 1344, 'label': '4D', 'order': 4, 'powers': [2, 13, 13], 'representative': 675, 'size': 6}
  • id: 116985827
    {'aut_label': '4E', 'centralizer': '28.g1.a1', 'counter': 14, 'group_counter': 8544, 'group_order': 1344, 'label': '4E', 'order': 4, 'powers': [2, 14, 14], 'representative': 943, 'size': 28}
  • id: 116985828
    {'aut_label': '4F', 'centralizer': '28.n1.a1', 'counter': 15, 'group_counter': 8544, 'group_order': 1344, 'label': '4F', 'order': 4, 'powers': [2, 15, 15], 'representative': 823, 'size': 28}
  • id: 116985829
    {'aut_label': '4E', 'centralizer': '28.g1.a1', 'counter': 16, 'group_counter': 8544, 'group_order': 1344, 'label': '4G', 'order': 4, 'powers': [2, 16, 16], 'representative': 942, 'size': 28}
  • id: 116985830
    {'aut_label': '4H', 'centralizer': '84.d1.a1', 'counter': 17, 'group_counter': 8544, 'group_order': 1344, 'label': '4H', 'order': 4, 'powers': [2, 17, 17], 'representative': 1133, 'size': 84}
  • id: 116985831
    {'aut_label': '4I', 'centralizer': '84.l1.a1', 'counter': 18, 'group_counter': 8544, 'group_order': 1344, 'label': '4I', 'order': 4, 'powers': [2, 18, 18], 'representative': 293, 'size': 84}
  • id: 116985832
    {'aut_label': '4H', 'centralizer': '84.d1.a1', 'counter': 19, 'group_counter': 8544, 'group_order': 1344, 'label': '4J', 'order': 4, 'powers': [2, 19, 19], 'representative': 460, 'size': 84}
  • id: 116985834
    {'aut_label': '6A', 'centralizer': '2.d1.a1', 'counter': 20, 'group_counter': 8544, 'group_order': 1344, 'label': '6A', 'order': 6, 'powers': [9, 2, 20], 'representative': 224, 'size': 2}
  • id: 116985835
    {'aut_label': '6B', 'centralizer': '4.d1.a1', 'counter': 21, 'group_counter': 8544, 'group_order': 1344, 'label': '6B', 'order': 6, 'powers': [9, 3, 21], 'representative': 785, 'size': 4}
  • id: 116985836
    {'aut_label': '6C', 'centralizer': '56.u1.a1', 'counter': 22, 'group_counter': 8544, 'group_order': 1344, 'label': '6C', 'order': 6, 'powers': [9, 7, 22], 'representative': 502, 'size': 56}
  • id: 116985837
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 23, 'group_counter': 8544, 'group_order': 1344, 'label': '7A1', 'order': 7, 'powers': [24, 25, 1], 'representative': 384, 'size': 2}
  • id: 116985838
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 24, 'group_counter': 8544, 'group_order': 1344, 'label': '7A2', 'order': 7, 'powers': [25, 23, 1], 'representative': 768, 'size': 2}
  • id: 116985839
    {'aut_label': '7A1', 'centralizer': '2.c1.a1', 'counter': 25, 'group_counter': 8544, 'group_order': 1344, 'label': '7A3', 'order': 7, 'powers': [23, 24, 1], 'representative': 1152, 'size': 2}
  • id: 116985840
    {'aut_label': '8A', 'centralizer': '4.k1.a1', 'counter': 26, 'group_counter': 8544, 'group_order': 1344, 'label': '8A', 'order': 8, 'powers': [10, 26, 26], 'representative': 168, 'size': 4}
  • id: 116985841
    {'aut_label': '8A', 'centralizer': '4.k1.b1', 'counter': 27, 'group_counter': 8544, 'group_order': 1344, 'label': '8B', 'order': 8, 'powers': [10, 27, 27], 'representative': 169, 'size': 4}
  • id: 116985842
    {'aut_label': '8C', 'centralizer': '12.r1.a1', 'counter': 28, 'group_counter': 8544, 'group_order': 1344, 'label': '8C', 'order': 8, 'powers': [10, 28, 28], 'representative': 58, 'size': 12}
  • id: 116985843
    {'aut_label': '8C', 'centralizer': '12.r1.b1', 'counter': 29, 'group_counter': 8544, 'group_order': 1344, 'label': '8D', 'order': 8, 'powers': [10, 29, 29], 'representative': 59, 'size': 12}
  • id: 116985845
    {'aut_label': '12A', 'centralizer': '4.b1.a1', 'counter': 30, 'group_counter': 8544, 'group_order': 1344, 'label': '12A', 'order': 12, 'powers': [20, 11, 30], 'representative': 1121, 'size': 4}
  • id: 116985846
    {'aut_label': '12B', 'centralizer': '4.f1.a1', 'counter': 31, 'group_counter': 8544, 'group_order': 1344, 'label': '12B', 'order': 12, 'powers': [20, 10, 31], 'representative': 112, 'size': 4}
  • id: 116985847
    {'aut_label': '12C', 'centralizer': '56.l1.a1', 'counter': 32, 'group_counter': 8544, 'group_order': 1344, 'label': '12C', 'order': 12, 'powers': [20, 14, 32], 'representative': 1167, 'size': 56}
  • id: 116985848
    {'aut_label': '12D', 'centralizer': '56.u1.a1', 'counter': 33, 'group_counter': 8544, 'group_order': 1344, 'label': '12D', 'order': 12, 'powers': [20, 15, 33], 'representative': 1047, 'size': 56}
  • id: 116985849
    {'aut_label': '12C', 'centralizer': '56.l1.a1', 'counter': 34, 'group_counter': 8544, 'group_order': 1344, 'label': '12E', 'order': 12, 'powers': [20, 16, 34], 'representative': 1166, 'size': 56}
  • id: 116985850
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 35, 'group_counter': 8544, 'group_order': 1344, 'label': '14A1', 'order': 14, 'powers': [23, 36, 2], 'representative': 480, 'size': 2}
  • id: 116985851
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 36, 'group_counter': 8544, 'group_order': 1344, 'label': '14A3', 'order': 14, 'powers': [25, 37, 2], 'representative': 96, 'size': 2}
  • id: 116985852
    {'aut_label': '14A1', 'centralizer': '2.c1.a1', 'counter': 37, 'group_counter': 8544, 'group_order': 1344, 'label': '14A5', 'order': 14, 'powers': [24, 35, 2], 'representative': 1056, 'size': 2}
  • id: 116985853
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 38, 'group_counter': 8544, 'group_order': 1344, 'label': '14B1', 'order': 14, 'powers': [24, 39, 3], 'representative': 721, 'size': 4}
  • id: 116985854
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 39, 'group_counter': 8544, 'group_order': 1344, 'label': '14B3', 'order': 14, 'powers': [23, 40, 3], 'representative': 145, 'size': 4}
  • id: 116985856
    {'aut_label': '14B1', 'centralizer': '4.a1.a1', 'counter': 40, 'group_counter': 8544, 'group_order': 1344, 'label': '14B5', 'order': 14, 'powers': [25, 38, 3], 'representative': 913, 'size': 4}
  • id: 116985857
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 41, 'group_counter': 8544, 'group_order': 1344, 'label': '14C1', 'order': 14, 'powers': [23, 42, 4], 'representative': 194, 'size': 6}
  • id: 116985858
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 42, 'group_counter': 8544, 'group_order': 1344, 'label': '14C3', 'order': 14, 'powers': [25, 43, 4], 'representative': 130, 'size': 6}
  • id: 116985859
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 43, 'group_counter': 8544, 'group_order': 1344, 'label': '14C5', 'order': 14, 'powers': [24, 41, 4], 'representative': 66, 'size': 6}
  • id: 116985860
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 44, 'group_counter': 8544, 'group_order': 1344, 'label': '14D1', 'order': 14, 'powers': [23, 45, 5], 'representative': 34, 'size': 6}
  • id: 116985861
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 45, 'group_counter': 8544, 'group_order': 1344, 'label': '14D3', 'order': 14, 'powers': [25, 46, 5], 'representative': 98, 'size': 6}
  • id: 116985862
    {'aut_label': '14C1', 'centralizer': '6.d1.a1', 'counter': 46, 'group_counter': 8544, 'group_order': 1344, 'label': '14D5', 'order': 14, 'powers': [24, 44, 5], 'representative': 162, 'size': 6}
  • id: 116985863
    {'aut_label': '14E1', 'centralizer': '12.g1.a1', 'counter': 47, 'group_counter': 8544, 'group_order': 1344, 'label': '14E1', 'order': 14, 'powers': [25, 48, 6], 'representative': 19, 'size': 12}
  • id: 116985864
    {'aut_label': '14E1', 'centralizer': '12.g1.a1', 'counter': 48, 'group_counter': 8544, 'group_order': 1344, 'label': '14E3', 'order': 14, 'powers': [24, 49, 6], 'representative': 51, 'size': 12}
  • id: 116985865
    {'aut_label': '14E1', 'centralizer': '12.g1.a1', 'counter': 49, 'group_counter': 8544, 'group_order': 1344, 'label': '14E5', 'order': 14, 'powers': [23, 47, 6], 'representative': 83, 'size': 12}
  • id: 116985867
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 50, 'group_counter': 8544, 'group_order': 1344, 'label': '21A1', 'order': 21, 'powers': [51, 24, 9], 'representative': 704, 'size': 4}
  • id: 116985868
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 51, 'group_counter': 8544, 'group_order': 1344, 'label': '21A2', 'order': 21, 'powers': [52, 25, 9], 'representative': 64, 'size': 4}
  • id: 116985869
    {'aut_label': '21A1', 'centralizer': '4.f1.a1', 'counter': 52, 'group_counter': 8544, 'group_order': 1344, 'label': '21A4', 'order': 21, 'powers': [50, 23, 9], 'representative': 128, 'size': 4}
  • id: 116985870
    {'aut_label': '24A', 'centralizer': '8.n1.a1', 'counter': 53, 'group_counter': 8544, 'group_order': 1344, 'label': '24A', 'order': 24, 'powers': [31, 26, 53], 'representative': 56, 'size': 8}
  • id: 116985871
    {'aut_label': '24A', 'centralizer': '8.n1.b1', 'counter': 54, 'group_counter': 8544, 'group_order': 1344, 'label': '24B', 'order': 24, 'powers': [31, 27, 54], 'representative': 57, 'size': 8}
  • id: 116985872
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 55, 'group_counter': 8544, 'group_order': 1344, 'label': '28A1', 'order': 28, 'powers': [35, 56, 10], 'representative': 912, 'size': 2}
  • id: 116985873
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 56, 'group_counter': 8544, 'group_order': 1344, 'label': '28A3', 'order': 28, 'powers': [36, 58, 10], 'representative': 48, 'size': 2}
  • id: 116985874
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 57, 'group_counter': 8544, 'group_order': 1344, 'label': '28A5', 'order': 28, 'powers': [37, 60, 10], 'representative': 528, 'size': 2}
  • id: 116985875
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 58, 'group_counter': 8544, 'group_order': 1344, 'label': '28A9', 'order': 28, 'powers': [37, 55, 10], 'representative': 144, 'size': 2}
  • id: 116985876
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 59, 'group_counter': 8544, 'group_order': 1344, 'label': '28A11', 'order': 28, 'powers': [36, 57, 10], 'representative': 624, 'size': 2}
  • id: 116985878
    {'aut_label': '28A1', 'centralizer': '2.c1.a1', 'counter': 60, 'group_counter': 8544, 'group_order': 1344, 'label': '28A13', 'order': 28, 'powers': [35, 59, 10], 'representative': 1104, 'size': 2}
  • id: 116985879
    {'aut_label': '28B1', 'centralizer': '4.a1.a1', 'counter': 61, 'group_counter': 8544, 'group_order': 1344, 'label': '28B1', 'order': 28, 'powers': [37, 62, 11], 'representative': 865, 'size': 4}
  • id: 116985880
    {'aut_label': '28B1', 'centralizer': '4.a1.a1', 'counter': 62, 'group_counter': 8544, 'group_order': 1344, 'label': '28B3', 'order': 28, 'powers': [35, 63, 11], 'representative': 577, 'size': 4}
  • id: 116985881
    {'aut_label': '28B1', 'centralizer': '4.a1.a1', 'counter': 63, 'group_counter': 8544, 'group_order': 1344, 'label': '28B5', 'order': 28, 'powers': [36, 61, 11], 'representative': 289, 'size': 4}
  • id: 116985882
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 64, 'group_counter': 8544, 'group_order': 1344, 'label': '28C1', 'order': 28, 'powers': [35, 65, 12], 'representative': 18, 'size': 6}
  • id: 116985883
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 65, 'group_counter': 8544, 'group_order': 1344, 'label': '28C3', 'order': 28, 'powers': [36, 67, 12], 'representative': 50, 'size': 6}
  • id: 116985884
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 66, 'group_counter': 8544, 'group_order': 1344, 'label': '28C5', 'order': 28, 'powers': [37, 69, 12], 'representative': 82, 'size': 6}
  • id: 116985885
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 67, 'group_counter': 8544, 'group_order': 1344, 'label': '28C9', 'order': 28, 'powers': [37, 64, 12], 'representative': 146, 'size': 6}
  • id: 116985886
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 68, 'group_counter': 8544, 'group_order': 1344, 'label': '28C11', 'order': 28, 'powers': [36, 66, 12], 'representative': 1170, 'size': 6}
  • id: 116985887
    {'aut_label': '28C1', 'centralizer': '6.d1.a1', 'counter': 69, 'group_counter': 8544, 'group_order': 1344, 'label': '28C13', 'order': 28, 'powers': [35, 68, 12], 'representative': 210, 'size': 6}
  • id: 116985889
    {'aut_label': '28D1', 'centralizer': '12.g1.a1', 'counter': 70, 'group_counter': 8544, 'group_order': 1344, 'label': '28D1', 'order': 28, 'powers': [37, 71, 13], 'representative': 195, 'size': 12}
  • id: 116985890
    {'aut_label': '28D1', 'centralizer': '12.g1.a1', 'counter': 71, 'group_counter': 8544, 'group_order': 1344, 'label': '28D3', 'order': 28, 'powers': [35, 72, 13], 'representative': 131, 'size': 12}
  • id: 116985891
    {'aut_label': '28D1', 'centralizer': '12.g1.a1', 'counter': 72, 'group_counter': 8544, 'group_order': 1344, 'label': '28D5', 'order': 28, 'powers': [36, 70, 13], 'representative': 67, 'size': 12}
  • id: 116985892
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 73, 'group_counter': 8544, 'group_order': 1344, 'label': '42A1', 'order': 42, 'powers': [50, 37, 20], 'representative': 800, 'size': 4}
  • id: 116985893
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 74, 'group_counter': 8544, 'group_order': 1344, 'label': '42A5', 'order': 42, 'powers': [51, 36, 20], 'representative': 1312, 'size': 4}
  • id: 116985894
    {'aut_label': '42A1', 'centralizer': '4.f1.a1', 'counter': 75, 'group_counter': 8544, 'group_order': 1344, 'label': '42A11', 'order': 42, 'powers': [52, 35, 20], 'representative': 736, 'size': 4}
  • id: 116985895
    {'aut_label': '42B1', 'centralizer': '8.b1.a1', 'counter': 76, 'group_counter': 8544, 'group_order': 1344, 'label': '42B1', 'order': 42, 'powers': [50, 38, 21], 'representative': 17, 'size': 8}
  • id: 116985896
    {'aut_label': '42B1', 'centralizer': '8.b1.a1', 'counter': 77, 'group_counter': 8544, 'group_order': 1344, 'label': '42B5', 'order': 42, 'powers': [51, 40, 21], 'representative': 81, 'size': 8}
  • id: 116985897
    {'aut_label': '42B1', 'centralizer': '8.b1.a1', 'counter': 78, 'group_counter': 8544, 'group_order': 1344, 'label': '42B11', 'order': 42, 'powers': [52, 39, 21], 'representative': 401, 'size': 8}
  • id: 116985898
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 79, 'group_counter': 8544, 'group_order': 1344, 'label': '56A1', 'order': 56, 'powers': [56, 80, 26], 'representative': 24, 'size': 4}
  • id: 116985900
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 80, 'group_counter': 8544, 'group_order': 1344, 'label': '56A3', 'order': 56, 'powers': [58, 82, 26], 'representative': 72, 'size': 4}
  • id: 116985901
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 81, 'group_counter': 8544, 'group_order': 1344, 'label': '56A5', 'order': 56, 'powers': [60, 84, 26], 'representative': 120, 'size': 4}
  • id: 116985902
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 82, 'group_counter': 8544, 'group_order': 1344, 'label': '56A9', 'order': 56, 'powers': [55, 79, 26], 'representative': 216, 'size': 4}
  • id: 116985903
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 83, 'group_counter': 8544, 'group_order': 1344, 'label': '56A11', 'order': 56, 'powers': [57, 81, 26], 'representative': 264, 'size': 4}
  • id: 116985904
    {'aut_label': '56A1', 'centralizer': '4.k1.a1', 'counter': 84, 'group_counter': 8544, 'group_order': 1344, 'label': '56A13', 'order': 56, 'powers': [59, 83, 26], 'representative': 312, 'size': 4}
  • id: 116985905
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 85, 'group_counter': 8544, 'group_order': 1344, 'label': '56B1', 'order': 56, 'powers': [56, 86, 27], 'representative': 25, 'size': 4}
  • id: 116985906
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 86, 'group_counter': 8544, 'group_order': 1344, 'label': '56B3', 'order': 56, 'powers': [58, 88, 27], 'representative': 73, 'size': 4}
  • id: 116985907
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 87, 'group_counter': 8544, 'group_order': 1344, 'label': '56B5', 'order': 56, 'powers': [60, 90, 27], 'representative': 121, 'size': 4}
  • id: 116985908
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 88, 'group_counter': 8544, 'group_order': 1344, 'label': '56B9', 'order': 56, 'powers': [55, 85, 27], 'representative': 217, 'size': 4}
  • id: 116985909
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 89, 'group_counter': 8544, 'group_order': 1344, 'label': '56B11', 'order': 56, 'powers': [57, 87, 27], 'representative': 265, 'size': 4}
  • id: 116985911
    {'aut_label': '56A1', 'centralizer': '4.k1.b1', 'counter': 90, 'group_counter': 8544, 'group_order': 1344, 'label': '56B13', 'order': 56, 'powers': [59, 89, 27], 'representative': 313, 'size': 4}
  • id: 116985912
    {'aut_label': '56C1', 'centralizer': '12.r1.a1', 'counter': 91, 'group_counter': 8544, 'group_order': 1344, 'label': '56C1', 'order': 56, 'powers': [55, 92, 28], 'representative': 10, 'size': 12}
  • id: 116985913
    {'aut_label': '56C1', 'centralizer': '12.r1.a1', 'counter': 92, 'group_counter': 8544, 'group_order': 1344, 'label': '56C3', 'order': 56, 'powers': [56, 94, 28], 'representative': 202, 'size': 12}
  • id: 116985914
    {'aut_label': '56C1', 'centralizer': '12.r1.a1', 'counter': 93, 'group_counter': 8544, 'group_order': 1344, 'label': '56C5', 'order': 56, 'powers': [57, 96, 28], 'representative': 42, 'size': 12}
  • id: 116985915
    {'aut_label': '56C1', 'centralizer': '12.r1.a1', 'counter': 94, 'group_counter': 8544, 'group_order': 1344, 'label': '56C9', 'order': 56, 'powers': [58, 91, 28], 'representative': 74, 'size': 12}
  • id: 116985916
    {'aut_label': '56C1', 'centralizer': '12.r1.a1', 'counter': 95, 'group_counter': 8544, 'group_order': 1344, 'label': '56C11', 'order': 56, 'powers': [59, 93, 28], 'representative': 138, 'size': 12}
  • id: 116985917
    {'aut_label': '56C1', 'centralizer': '12.r1.a1', 'counter': 96, 'group_counter': 8544, 'group_order': 1344, 'label': '56C13', 'order': 56, 'powers': [60, 95, 28], 'representative': 778, 'size': 12}
  • id: 116985918
    {'aut_label': '56C1', 'centralizer': '12.r1.b1', 'counter': 97, 'group_counter': 8544, 'group_order': 1344, 'label': '56D1', 'order': 56, 'powers': [55, 98, 29], 'representative': 11, 'size': 12}
  • id: 116985919
    {'aut_label': '56C1', 'centralizer': '12.r1.b1', 'counter': 98, 'group_counter': 8544, 'group_order': 1344, 'label': '56D3', 'order': 56, 'powers': [56, 100, 29], 'representative': 203, 'size': 12}
  • id: 116985920
    {'aut_label': '56C1', 'centralizer': '12.r1.b1', 'counter': 99, 'group_counter': 8544, 'group_order': 1344, 'label': '56D5', 'order': 56, 'powers': [57, 102, 29], 'representative': 43, 'size': 12}
  • id: 116985800
    {'aut_label': '56C1', 'centralizer': '12.r1.b1', 'counter': 100, 'group_counter': 8544, 'group_order': 1344, 'label': '56D9', 'order': 56, 'powers': [58, 97, 29], 'representative': 75, 'size': 12}
  • id: 116985801
    {'aut_label': '56C1', 'centralizer': '12.r1.b1', 'counter': 101, 'group_counter': 8544, 'group_order': 1344, 'label': '56D11', 'order': 56, 'powers': [59, 99, 29], 'representative': 139, 'size': 12}
  • id: 116985802
    {'aut_label': '56C1', 'centralizer': '12.r1.b1', 'counter': 102, 'group_counter': 8544, 'group_order': 1344, 'label': '56D13', 'order': 56, 'powers': [60, 101, 29], 'representative': 779, 'size': 12}
  • id: 116985803
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 103, 'group_counter': 8544, 'group_order': 1344, 'label': '84A1', 'order': 84, 'powers': [74, 56, 31], 'representative': 16, 'size': 4}
  • id: 116985804
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 104, 'group_counter': 8544, 'group_order': 1344, 'label': '84A5', 'order': 84, 'powers': [75, 60, 31], 'representative': 80, 'size': 4}
  • id: 116985805
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 105, 'group_counter': 8544, 'group_order': 1344, 'label': '84A11', 'order': 84, 'powers': [73, 57, 31], 'representative': 176, 'size': 4}
  • id: 116985806
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 106, 'group_counter': 8544, 'group_order': 1344, 'label': '84A13', 'order': 84, 'powers': [74, 59, 31], 'representative': 208, 'size': 4}
  • id: 116985807
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 107, 'group_counter': 8544, 'group_order': 1344, 'label': '84A19', 'order': 84, 'powers': [75, 55, 31], 'representative': 304, 'size': 4}
  • id: 116985808
    {'aut_label': '84A1', 'centralizer': '4.f1.a1', 'counter': 108, 'group_counter': 8544, 'group_order': 1344, 'label': '84A25', 'order': 84, 'powers': [73, 58, 31], 'representative': 400, 'size': 4}
  • id: 116985809
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 109, 'group_counter': 8544, 'group_order': 1344, 'label': '84B1', 'order': 84, 'powers': [73, 61, 30], 'representative': 65, 'size': 8}
  • id: 116985811
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 110, 'group_counter': 8544, 'group_order': 1344, 'label': '84B5', 'order': 84, 'powers': [74, 63, 30], 'representative': 129, 'size': 8}
  • id: 116985812
    {'aut_label': '84B1', 'centralizer': '8.b1.a1', 'counter': 111, 'group_counter': 8544, 'group_order': 1344, 'label': '84B11', 'order': 84, 'powers': [75, 62, 30], 'representative': 33, 'size': 8}
  • id: 116985813
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 112, 'group_counter': 8544, 'group_order': 1344, 'label': '168A1', 'order': 168, 'powers': [103, 79, 53], 'representative': 8, 'size': 8}
  • id: 116985814
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 113, 'group_counter': 8544, 'group_order': 1344, 'label': '168A5', 'order': 168, 'powers': [104, 81, 53], 'representative': 40, 'size': 8}
  • id: 116985815
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 114, 'group_counter': 8544, 'group_order': 1344, 'label': '168A11', 'order': 168, 'powers': [105, 83, 53], 'representative': 136, 'size': 8}
  • id: 116985816
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 115, 'group_counter': 8544, 'group_order': 1344, 'label': '168A13', 'order': 168, 'powers': [106, 84, 53], 'representative': 776, 'size': 8}
  • id: 116985817
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 116, 'group_counter': 8544, 'group_order': 1344, 'label': '168A19', 'order': 168, 'powers': [107, 82, 53], 'representative': 968, 'size': 8}
  • id: 116985818
    {'aut_label': '168A1', 'centralizer': '8.n1.a1', 'counter': 117, 'group_counter': 8544, 'group_order': 1344, 'label': '168A25', 'order': 168, 'powers': [108, 80, 53], 'representative': 200, 'size': 8}
  • id: 116985819
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 118, 'group_counter': 8544, 'group_order': 1344, 'label': '168B1', 'order': 168, 'powers': [103, 85, 54], 'representative': 9, 'size': 8}
  • id: 116985820
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 119, 'group_counter': 8544, 'group_order': 1344, 'label': '168B5', 'order': 168, 'powers': [104, 87, 54], 'representative': 41, 'size': 8}
  • id: 116985822
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 120, 'group_counter': 8544, 'group_order': 1344, 'label': '168B11', 'order': 168, 'powers': [105, 89, 54], 'representative': 137, 'size': 8}
  • id: 116985823
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 121, 'group_counter': 8544, 'group_order': 1344, 'label': '168B13', 'order': 168, 'powers': [106, 90, 54], 'representative': 777, 'size': 8}
  • id: 116985824
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 122, 'group_counter': 8544, 'group_order': 1344, 'label': '168B19', 'order': 168, 'powers': [107, 88, 54], 'representative': 969, 'size': 8}
  • id: 116985825
    {'aut_label': '168A1', 'centralizer': '8.n1.b1', 'counter': 123, 'group_counter': 8544, 'group_order': 1344, 'label': '168B25', 'order': 168, 'powers': [108, 86, 54], 'representative': 201, '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: 6053114
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053125
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6053136
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1c', '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, 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: 6053147
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1d', '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, 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: 6053158
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1e', '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, -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: 6053164
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1f', '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, 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: 6053165
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1g', '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, -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: 6053166
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1h', '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, -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: 6053167
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6053115
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053116
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053117
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053118
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053119
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053120
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053121
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053122
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 2, 0, -1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053123
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 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, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053124
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -2, 0, 0, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 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, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053126
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, -2, 0, 0, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 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, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053127
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 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, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053128
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, -2, 0, -1, 2, -2, 0, 0, -2, 2, 2, 0, 0, 0, -1, 1, 1, 2, 2, 2, -2, 2, 0, 0, 1, -1, 1, -1, -1, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 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, -1, -1, -1, 1, 1, 1, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6053129
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, -2, 0, -1, 2, -2, 0, 0, 2, 2, -2, 0, 0, 0, -1, 1, 1, 2, 2, 2, 2, -2, 0, 0, 1, -1, -1, -1, 1, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 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, -1, -1, -1, 1, 1, 1, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6053130
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 2, 0, -1, 2, -2, 0, 0, -2, -2, 2, 0, 0, 0, -1, 1, -1, 2, 2, 2, 2, -2, 0, 0, 1, -1, 1, 1, -1, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 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, -1, -1, -1, 1, 1, 1, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6053131
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 2, 0, -1, 2, -2, 0, 0, 2, -2, -2, 0, 0, 0, -1, 1, -1, 2, 2, 2, -2, 2, 0, 0, 1, -1, -1, 1, 1, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 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, -1, -1, -1, 1, 1, 1, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6053132
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, -2, 0, -1, 2, 2, 0, 0, -2, -2, -2, 0, 0, 0, -1, -1, 1, 2, 2, 2, 2, 2, 0, 0, -1, -1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053133
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, -2, 0, -1, 2, 2, 0, 0, 2, -2, 2, 0, 0, 0, -1, -1, 1, 2, 2, 2, -2, -2, 0, 0, -1, -1, -1, 1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053134
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 2, 0, -1, 2, 2, 0, 0, -2, 2, -2, 0, 0, 0, -1, -1, -1, 2, 2, 2, -2, -2, 0, 0, -1, -1, 1, -1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053149
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, 0, 0, 0, -2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 4, 4, 4, 0, 0, 0, 0, -2, 2, 0, 0, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 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, -2, -2, -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, 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: 6053150
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, 0, 0, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 4, 4, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 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, -2, -2, -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, 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: 6053151
    {'cdim': 4, 'counter': 43, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4c', 'multiplicity': 1, 'nt': [16, 32], 'qdim': 4, 'qvalues': [4, -4, 0, -4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, -4, -4, 4, -4, 4, 4, 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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 6053152
    {'cdim': 4, 'counter': 44, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4d', 'multiplicity': 1, 'nt': [16, 32], 'qdim': 4, 'qvalues': [4, -4, 0, 4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 4, 4, -4, 4, -4, -4, 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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 6053135
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2m', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, -1, -1, -1, 6, 6, 6, 6, 6, 6, 0, 0, 0, -1, -1, -1, -1, -1, -1, -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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053137
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2n', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -6, 6, 0, 0, 6, 6, -6, -6, 6, 0, 0, 0, 0, 0, 0, 6, -6, 0, -1, -1, -1, -6, 6, 6, -6, -6, 6, 0, 0, 0, -1, -1, -1, 1, 1, 1, 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, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6053138
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2o', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -6, 6, 0, 0, 6, 6, -6, -6, 6, 0, 0, 0, 0, 0, 0, 6, -6, 0, -1, -1, -1, 6, -6, -6, 6, -6, 6, 0, 0, 0, -1, -1, -1, 1, 1, 1, 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, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6053139
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2p', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 6, -6, 0, 0, 6, 6, -6, 6, -6, 0, 0, 0, 0, 0, 0, 6, -6, 0, -1, -1, -1, -6, 6, -6, 6, -6, 6, 0, 0, 0, -1, -1, -1, 1, 1, 1, -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, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6053140
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2q', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 6, -6, 0, 0, 6, 6, -6, 6, -6, 0, 0, 0, 0, 0, 0, 6, -6, 0, -1, -1, -1, 6, -6, 6, -6, -6, 6, 0, 0, 0, -1, -1, -1, 1, 1, 1, -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, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6053141
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2r', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -6, -6, 0, 0, 6, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 6, 6, 0, -1, -1, -1, -6, -6, 6, 6, 6, 6, 0, 0, 0, -1, -1, -1, -1, -1, -1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053142
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2s', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, -6, -6, -6, 0, 0, 6, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 6, 6, 0, -1, -1, -1, 6, 6, -6, -6, 6, 6, 0, 0, 0, -1, -1, -1, -1, -1, -1, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053143
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2t', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, -1, -1, -1, -6, -6, -6, -6, 6, 6, 0, 0, 0, -1, -1, -1, -1, -1, -1, -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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053162
    {'cdim': 8, 'counter': 53, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.8a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 6053144
    {'cdim': 2, 'counter': 37, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2u', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, -12, -12, -12, 12, 0, 0, 12, -12, 12, 12, -12, 0, 0, 0, 0, 0, 0, 12, -12, 0, -2, -2, -2, 0, 0, 0, 0, 12, -12, 0, 0, 0, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 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, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053145
    {'cdim': 2, 'counter': 38, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2v', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, -12, 12, 12, -12, 0, 0, 12, -12, 12, -12, 12, 0, 0, 0, 0, 0, 0, 12, -12, 0, -2, -2, -2, 0, 0, 0, 0, 12, -12, 0, 0, 0, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 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, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053146
    {'cdim': 2, 'counter': 39, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2w', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, 12, -12, -12, -12, 0, 0, 12, -12, -12, 12, 12, 0, 0, 0, 0, 0, 0, 12, 12, 0, -2, -2, -2, 0, 0, 0, 0, -12, -12, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 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, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053148
    {'cdim': 2, 'counter': 40, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.2x', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 12, 12, 0, 0, 12, -12, -12, -12, -12, 0, 0, 0, 0, 0, 0, 12, 12, 0, -2, -2, -2, 0, 0, 0, 0, -12, -12, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 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, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 6053153
    {'cdim': 4, 'counter': 45, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4e', 'multiplicity': 3, 'nt': [21, 8], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, 0, -6, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, -2, -2, -2, 12, 12, 0, 0, -6, -6, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 6053154
    {'cdim': 4, 'counter': 46, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4f', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 0, 0, 0, 0, -6, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, -2, -2, -2, -12, 12, 0, 0, 6, -6, 0, 0, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, -1, -1, -1, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 6053155
    {'cdim': 4, 'counter': 47, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4g', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, -12, 0, 0, 0, 0, 0, -6, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, -2, -2, -2, 12, -12, 0, 0, 6, -6, 0, 0, 0, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, -1, -1, -1, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 6053156
    {'cdim': 4, 'counter': 48, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4h', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 12, 0, 0, 0, 0, 0, -6, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, -2, -2, -2, -12, -12, 0, 0, -6, -6, 0, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 6053157
    {'cdim': 4, 'counter': 49, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4i', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, -24, 0, 0, 0, 0, 0, -12, -24, 24, 0, 0, 0, 0, 0, 0, 0, 0, -12, 12, 0, -4, -4, -4, 0, 0, 0, 0, -12, 12, 0, 0, 0, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 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, 2, 2, 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, -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: 6053159
    {'cdim': 4, 'counter': 50, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4j', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, 24, 0, 0, 0, 0, 0, -12, -24, -24, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 0, -4, -4, -4, 0, 0, 0, 0, 12, 12, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 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, 2, 2, 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, -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: 6053160
    {'cdim': 4, 'counter': 51, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4k', 'multiplicity': 6, 'nt': [112, 0], 'qdim': 24, 'qvalues': [24, -24, 0, -24, 24, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 4, 4, -4, 4, -4, -4, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 6053161
    {'cdim': 4, 'counter': 52, 'faithful': False, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.4l', 'multiplicity': 6, 'nt': [112, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 24, -24, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, -4, -4, 4, -4, 4, 4, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 6053163
    {'cdim': 8, 'counter': 54, 'faithful': True, 'group': '1344.8544', 'group_order': 1344, 'image': None, 'label': '1344.8544.8b', 'multiplicity': 6, 'nt': [336, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 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, -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, 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: 12577419
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1344, 'label': '1344.8544.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 12577454
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.b1', 'kernel_order': 672, 'label': '1344.8544.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 12577465
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  • id: 12577476
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  • id: 12577487
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  • id: 12577498
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  • id: 12577509
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  • id: 12577520
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  • id: 12577531
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  • id: 12577420
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  • id: 12577431
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 672, 'label': '1344.8544.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 12577442
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  • id: 12577447
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  • id: 12577448
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  • id: 12577449
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  • id: 12577450
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  • id: 12577451
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  • id: 12577452
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  • id: 12577453
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  • id: 12577455
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  • id: 12577456
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  • id: 12577457
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  • id: 12577458
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  • id: 12577459
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  • id: 12577460
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  • id: 12577461
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  • id: 12577462
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  • id: 12577463
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 224, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 112, 'label': '1344.8544.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 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]], [[2, 0]], [[2, 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]], [[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]], [[-1, 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]], [[-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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 12577464
    {'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': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.8544.2m1', 'nt': [7, 2], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 1], [1, -1]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[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, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 12577466
    {'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': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.8544.2m2', 'nt': [7, 2], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 3], [1, -3]], [[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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[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, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577467
    {'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': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 96, 'label': '1344.8544.2m3', 'nt': [7, 2], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 2], [1, -2]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[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, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 12577468
    {'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': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.8544.2n1', 'nt': [14, 3], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 1], [1, -1]], [[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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[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, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]]]}
  • id: 12577469
    {'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': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.8544.2n2', 'nt': [14, 3], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 3], [1, -3]], [[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, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[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, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577470
    {'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': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.b1', 'kernel_order': 48, 'label': '1344.8544.2n3', 'nt': [14, 3], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 2], [1, -2]], [[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, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[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, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]]]}
  • id: 12577471
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 35, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.e1.a1', 'kernel_order': 48, 'label': '1344.8544.2o1', 'nt': [14, 3], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 1], [1, -1]], [[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, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-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, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 12577472
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  • id: 12577473
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  • id: 12577474
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  • id: 12577475
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  • id: 12577477
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  • id: 12577478
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  • id: 12577479
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  • id: 12577480
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  • id: 12577481
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  • id: 12577482
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  • id: 12577483
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  • id: 12577484
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  • id: 12577485
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  • id: 12577486
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 49, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.b1.a1', 'kernel_order': 48, 'label': '1344.8544.2s3', 'nt': [14, 3], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[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, 2], [1, -2]], [[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, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[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, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 12577488
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 50, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.8544.2t1', 'nt': [14, 3], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 1], [1, -1]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-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, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 12577489
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 51, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.8544.2t2', 'nt': [14, 3], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 3], [1, -3]], [[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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-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, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12577490
    {'center': '14.a1.a1', 'center_index': 14, 'center_order': 96, 'counter': 52, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 48, 'label': '1344.8544.2t3', 'nt': [14, 3], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[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, 2], [1, -2]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-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, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 12577491
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  • id: 12577492
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  • id: 12577493
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 55, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8544.2u3', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-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, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[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, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]]]}
  • id: 12577494
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  • id: 12577495
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 57, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8544.2u5', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[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, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-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, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]]]}
  • id: 12577496
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 58, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.g1.a1', 'kernel_order': 24, 'label': '1344.8544.2u6', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[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, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-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, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]]]}
  • id: 12577497
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 59, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8544.2v1', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-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, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-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, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577499
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  • id: 12577500
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 61, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8544.2v3', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[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, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[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, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]]]}
  • id: 12577501
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 62, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8544.2v4', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[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, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[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, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]]]}
  • id: 12577502
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 63, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.e1.a1', 'kernel_order': 24, 'label': '1344.8544.2v5', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-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, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-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, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]]]}
  • id: 12577503
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  • id: 12577504
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 65, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.8544.2w1', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[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, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-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, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12577505
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 66, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.8544.2w2', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[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, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-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, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577506
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 67, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.8544.2w3', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-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, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[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, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]]]}
  • id: 12577507
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  • id: 12577508
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 69, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.8544.2w5', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[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, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-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, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]]]}
  • id: 12577510
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 70, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.c1.a1', 'kernel_order': 24, 'label': '1344.8544.2w6', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[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, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-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, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]]]}
  • id: 12577511
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 71, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8544.2x1', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-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, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-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, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12577512
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 72, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8544.2x2', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-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, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-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, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577513
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 73, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8544.2x3', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[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, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[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, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]]]}
  • id: 12577514
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 74, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8544.2x4', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[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, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[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, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]]]}
  • id: 12577515
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 75, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8544.2x5', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-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, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-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, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]]]}
  • id: 12577516
    {'center': '28.a1.a1', 'center_index': 28, 'center_order': 48, 'counter': 76, 'cyclotomic_n': 28, 'dim': 2, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '56.5', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1.a1', 'kernel_order': 24, 'label': '1344.8544.2x6', 'nt': [28, 10], 'q_character': None, 'values': [[[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-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, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-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, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]]]}
  • id: 12577517
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 56, 'counter': 77, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 28, 'label': '1344.8544.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 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]], [[-4, 0]], [[-4, 0]], [[-4, 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]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 12577518
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 56, 'counter': 78, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 28, 'label': '1344.8544.4b', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 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]], [[4, 0]], [[4, 0]], [[4, 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]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 12577519
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 84, 'counter': 79, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.b1.b1', 'kernel_order': 42, 'label': '1344.8544.4c', 'nt': [16, 32], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[-4, 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]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-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]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 12577521
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 84, 'counter': 80, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.b1.a1', 'kernel_order': 42, 'label': '1344.8544.4d', 'nt': [16, 32], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[-4, 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]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[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]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 12577522
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 81, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.8544.4e1', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[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]], [[-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, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 12577523
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 82, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.8544.4e2', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[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]], [[-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, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12577524
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 83, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '84.8', 'image_order': 84, 'indicator': 1, 'kernel': '84.a1.a1', 'kernel_order': 16, 'label': '1344.8544.4e3', 'nt': [21, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[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]], [[-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, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 12577525
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 84, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.8544.4f1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[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]], [[-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, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 12577526
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 85, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.8544.4f2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[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]], [[-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, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12577527
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 86, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.b1', 'kernel_order': 8, 'label': '1344.8544.4f3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[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]], [[-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, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[-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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 12577528
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 87, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.a1', 'kernel_order': 8, 'label': '1344.8544.4g1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[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]], [[-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, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]]]}
  • id: 12577529
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 88, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.a1', 'kernel_order': 8, 'label': '1344.8544.4g2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[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]], [[-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, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577530
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 89, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1.a1', 'kernel_order': 8, 'label': '1344.8544.4g3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[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]], [[-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, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]]]}
  • id: 12577532
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 90, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.8544.4h1', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[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]], [[-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, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 12577533
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 91, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.8544.4h2', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[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]], [[-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, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-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]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577534
    {'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 92, 'cyclotomic_n': 7, 'dim': 4, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '168.50', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 8, 'label': '1344.8544.4h3', 'nt': [42, 36], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[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]], [[-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, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 2], [-2, -2]], [[-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]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 12577535
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 93, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8544.4i1', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-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]], [[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, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[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]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 5], [-2, -5]], [[-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]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12577536
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 94, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8544.4i2', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-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]], [[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, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[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]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 5], [2, -5]], [[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]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577537
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 95, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8544.4i3', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-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]], [[-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, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[-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]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[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]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]]]}
  • id: 12577538
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 96, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8544.4i4', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-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]], [[-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, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[-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]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-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]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]]]}
  • id: 12577539
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 97, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8544.4i5', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[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]], [[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, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[-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]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[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]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]]]}
  • id: 12577540
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 98, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1.a1', 'kernel_order': 4, 'label': '1344.8544.4i6', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[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]], [[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, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[-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]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-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]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]]]}
  • id: 12577541
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 99, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8544.4j1', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-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]], [[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, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-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]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[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]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]]]}
  • id: 12577421
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 100, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8544.4j2', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-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]], [[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, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-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]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-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]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]]]}
  • id: 12577422
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 101, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8544.4j3', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-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]], [[-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, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[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]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[-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]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]]]}
  • id: 12577423
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 102, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8544.4j4', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-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]], [[-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, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[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]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[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]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]]]}
  • id: 12577424
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 103, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8544.4j5', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[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]], [[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, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[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]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[-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]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]]]}
  • id: 12577425
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 104, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '336.149', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.8544.4j6', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[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]], [[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, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[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]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 5], [2, -5]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[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]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]]]}
  • id: 12577426
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 105, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.b1', 'kernel_order': 6, 'label': '1344.8544.4k1', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[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]], [[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, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[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: 12577427
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 106, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.b1', 'kernel_order': 6, 'label': '1344.8544.4k2', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[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]], [[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, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-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: 12577428
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 107, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.b1', 'kernel_order': 6, 'label': '1344.8544.4k3', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[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]], [[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, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577429
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 108, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.b1', 'kernel_order': 6, 'label': '1344.8544.4k4', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[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]], [[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, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577430
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 109, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.b1', 'kernel_order': 6, 'label': '1344.8544.4k5', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[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]], [[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, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-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: 12577432
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 110, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.b1', 'kernel_order': 6, 'label': '1344.8544.4k6', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[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]], [[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, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[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: 12577433
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 111, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.a1', 'kernel_order': 6, 'label': '1344.8544.4l1', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[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]], [[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, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[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: 12577434
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 112, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.a1', 'kernel_order': 6, 'label': '1344.8544.4l2', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[0, 0]], [[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]], [[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, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-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: 12577435
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 113, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.a1', 'kernel_order': 6, 'label': '1344.8544.4l3', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[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]], [[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, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[2, 5], [2, -5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577436
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 114, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.a1', 'kernel_order': 6, 'label': '1344.8544.4l4', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 4], [-2, -4]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[0, 0]], [[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]], [[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, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577437
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 115, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.a1', 'kernel_order': 6, 'label': '1344.8544.4l5', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[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]], [[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, 1], [2, -1]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, -5]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 1], [2, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-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: 12577438
    {'center': '112.b1.a1', 'center_index': 112, 'center_order': 12, 'counter': 116, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '224.104', 'image_order': 224, 'indicator': -1, 'kernel': '224.b1.a1', 'kernel_order': 6, 'label': '1344.8544.4l6', 'nt': [112, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[-4, 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, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[0, 0]], [[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]], [[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, 1], [-2, -1]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, -5]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 1], [-2, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[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: 12577439
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 14, 'counter': 117, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '192.1335', 'image_order': 192, 'indicator': -1, 'kernel': '192.a1.a1', 'kernel_order': 7, 'label': '1344.8544.8a', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 12577440
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 118, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8544', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8544.8b1', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[4, 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]], [[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]], [[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, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3], [-2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-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: 12577441
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 119, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8544', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8544.8b2', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[4, 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]], [[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]], [[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, 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]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3], [2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[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: 12577443
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 120, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8544', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8544.8b3', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[4, 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]], [[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]], [[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, 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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [2, -5]], [[-2, 3], [-2, -3]], [[-2, 5], [-2, -5]], [[2, 1], [2, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577444
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 121, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8544', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8544.8b4', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[4, 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]], [[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]], [[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, 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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [-2, -5]], [[2, 3], [2, -3]], [[2, 5], [2, -5]], [[-2, 1], [-2, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 12577445
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 122, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8544', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8544.8b5', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[4, 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]], [[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]], [[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, 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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [-2, -5]], [[-2, 1], [-2, -1]], [[-2, 3], [-2, -3]], [[2, 5], [2, -5]], [[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: 12577446
    {'center': '672.a1.a1', 'center_index': 672, 'center_order': 2, 'counter': 123, 'cyclotomic_n': 28, 'dim': 8, 'faithful': True, 'field': [-7, 0, 14, 0, -7, 0, 1], 'group': '1344.8544', 'group_counter': 8544, 'group_order': 1344, 'image': None, 'image_isoclass': '1344.8544', 'image_order': 1344, 'indicator': -1, 'kernel': '1344.a1.a1', 'kernel_order': 1, 'label': '1344.8544.8b6', 'nt': [336, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[4, 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]], [[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]], [[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, 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]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [2, -5]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[-2, 5], [-2, -5]], [[-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]]]}
• 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: 74051686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1344, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '1344.8544.1.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': '1344.8544', 'subgroup_hash': 8544, 'subgroup_order': 1344, 'subgroup_tex': 'C_{168}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74051797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '672.1144', 'subgroup_hash': 1144, 'subgroup_order': 672, 'subgroup_tex': 'D_{28}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.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': '672.1131', 'subgroup_hash': 1131, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74052019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 672, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.885', 'subgroup_hash': 885, 'subgroup_order': 672, 'subgroup_tex': 'C_{56}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 672, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.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': '672.802', 'subgroup_hash': 802, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': '672.457', 'subgroup_hash': 457, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.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': '672.459', 'subgroup_hash': 459, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 672, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.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': '672.974', 'subgroup_hash': 974, 'subgroup_order': 672, 'subgroup_tex': 'C_4.D_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74052191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1.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': '672.395', 'subgroup_hash': 395, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.h1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.395', 'subgroup_hash': 395, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.i1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.i1.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': '672.406', 'subgroup_hash': 406, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.i1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.406', 'subgroup_hash': 406, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.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': '672.418', 'subgroup_hash': 418, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.j1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.418', 'subgroup_hash': 418, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.k1.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': '672.407', 'subgroup_hash': 407, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 672, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.2.k1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.407', 'subgroup_hash': 407, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 224, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '1344.8544.3.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': '448.1200', 'subgroup_hash': 1200, 'subgroup_order': 448, 'subgroup_tex': '\\OD_{16}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 336, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.185', 'subgroup_hash': 185, 'subgroup_order': 336, 'subgroup_tex': 'D_6\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.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: 74051798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.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': '336.197', 'subgroup_hash': 197, 'subgroup_order': 336, 'subgroup_tex': 'D_{84}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.174', 'subgroup_hash': 174, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.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': True, '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: 74051831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 336, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.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'], 'split': True, '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: 74051842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 336, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.80', 'subgroup_hash': 80, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.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': '336.149', 'subgroup_hash': 149, 'subgroup_order': 336, 'subgroup_tex': 'S_3\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.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': '336.140', 'subgroup_hash': 140, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.b1', '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': '336.140', 'subgroup_hash': 140, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.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': '336.140', 'subgroup_hash': 140, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 336, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.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': '336.74', 'subgroup_hash': 74, 'subgroup_order': 336, 'subgroup_tex': 'S_3\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74051909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 336, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.b1', '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': '336.74', 'subgroup_hash': 74, 'subgroup_order': 336, 'subgroup_tex': 'S_3\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74051920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1.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': '336.138', 'subgroup_hash': 138, 'subgroup_order': 336, 'subgroup_tex': 'D_{28}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1.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': '336.142', 'subgroup_hash': 142, 'subgroup_order': 336, 'subgroup_tex': 'D_{84}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.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': True, '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: 74051953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 336, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.b1', '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': True, '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: 74051964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 336, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.75', 'subgroup_hash': 75, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 336, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.75', 'subgroup_hash': 75, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.p1.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': True, '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: 74051997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.p1.b1', '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': True, '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: 74052008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.34', 'subgroup_hash': 34, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.34', 'subgroup_hash': 34, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.r1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.35', 'subgroup_hash': 35, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.r1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.35', 'subgroup_hash': 35, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.s1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.92', 'subgroup_hash': 92, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.s1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.92', 'subgroup_hash': 92, 'subgroup_order': 336, 'subgroup_tex': 'C_{168}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74052075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.t1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.62', 'subgroup_hash': 62, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 336, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.t1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.62', 'subgroup_hash': 62, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.u1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.39', 'subgroup_hash': 39, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.u1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.39', 'subgroup_hash': 39, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.v1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.39', 'subgroup_hash': 39, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.v1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.39', 'subgroup_hash': 39, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.94', 'subgroup_hash': 94, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 336, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.4.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.94', 'subgroup_hash': 94, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '336.162', 'subgroup_hash': 162, 'subgroup_order': 336, 'subgroup_tex': 'D_6:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.4.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '336.154', 'subgroup_hash': 154, 'subgroup_order': 336, 'subgroup_tex': 'D_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '336.152', 'subgroup_hash': 152, 'subgroup_order': 336, 'subgroup_tex': 'D_{14}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '336.160', 'subgroup_hash': 160, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '336.147', 'subgroup_hash': 147, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.4.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '336.144', 'subgroup_hash': 144, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.4.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.be1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 224, 'counter': 61, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1344.8544.6.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': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.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': '224.177', 'subgroup_hash': 177, 'subgroup_order': 224, 'subgroup_tex': 'D_{28}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74052162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.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': '224.174', 'subgroup_hash': 174, 'subgroup_order': 224, 'subgroup_tex': 'C_{14}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 74052163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 112, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '224.165', 'subgroup_hash': 165, 'subgroup_order': 224, 'subgroup_tex': 'C_{14}\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.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': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.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': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '224.97', 'subgroup_hash': 97, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '224.97', 'subgroup_hash': 97, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '224.100', 'subgroup_hash': 100, 'subgroup_order': 224, 'subgroup_tex': 'C_{14}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '224.100', 'subgroup_hash': 100, 'subgroup_order': 224, 'subgroup_tex': 'C_{14}:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 112, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.6.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '224.104', 'subgroup_hash': 104, 'subgroup_order': 224, 'subgroup_tex': 'C_4.D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 96, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1344.8544.7.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': '192.1335', 'subgroup_hash': 1335, 'subgroup_order': 192, 'subgroup_tex': 'Q_{16}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.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': '168.55', 'subgroup_hash': 55, 'subgroup_order': 168, 'subgroup_tex': 'D_6\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052178
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 168, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.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': ['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: 74052179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.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': '168.32', 'subgroup_hash': 32, 'subgroup_order': 168, 'subgroup_tex': 'C_6:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 168, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.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': '8.5', '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': [], 'split': False, '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: 74052182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.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': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.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': '8.5', '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': [], 'split': False, '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: 74052184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.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': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74052185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.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': [], '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: 74052186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 168, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.36', 'subgroup_hash': 36, 'subgroup_order': 168, 'subgroup_tex': 'D_{84}', 'supersolvable': True, 'sylow': 0}
  • id: 74052187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1.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': [], '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: 74052188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 168, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1.b1', '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': [], '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: 74052189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 168, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.k1.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': [], '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: 74052190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.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': [], 'split': False, '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: 74052192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 168, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.b1', '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': [], 'split': False, '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: 74052193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 168, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.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': [], 'split': False, '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: 74052194
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 168, 'counter': 92, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.6', 'subgroup_hash': 6, 'subgroup_order': 168, 'subgroup_tex': 'C_{168}', 'supersolvable': True, 'sylow': 0}
  • id: 74052195
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 168, 'counter': 93, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.8.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.b1', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.6', 'subgroup_hash': 6, 'subgroup_order': 168, 'subgroup_tex': 'C_{168}', 'supersolvable': True, 'sylow': 0}
  • id: 74052196
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 168, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.o1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.3', 'subgroup_hash': 3, 'subgroup_order': 168, 'subgroup_tex': 'C_3:C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052197
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 168, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.8.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.o1.b1', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.3', 'subgroup_hash': 3, 'subgroup_order': 168, 'subgroup_tex': 'C_3:C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74052198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.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': '168.28', 'subgroup_hash': 28, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.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': '168.38', 'subgroup_hash': 38, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.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': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74052201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '168.37', 'subgroup_hash': 37, 'subgroup_order': 168, 'subgroup_tex': 'C_{42}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '168.50', 'subgroup_hash': 50, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '168.13', 'subgroup_hash': 13, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.u1.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: 74051691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.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': '168.13', 'subgroup_hash': 13, 'subgroup_order': 168, 'subgroup_tex': 'C_6.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '168.17', 'subgroup_hash': 17, 'subgroup_order': 168, 'subgroup_tex': 'C_7:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74051694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.y1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.y1.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: 74051696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '168.16', 'subgroup_hash': 16, 'subgroup_order': 168, 'subgroup_tex': 'C_3:D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '168.35', 'subgroup_hash': 35, 'subgroup_order': 168, 'subgroup_tex': 'C_4\\times D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74051701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '168.14', 'subgroup_hash': 14, 'subgroup_order': 168, 'subgroup_tex': 'D_{21}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 84, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '168.24', 'subgroup_hash': 24, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bg1.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: 74051706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 84, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.8.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.bi1.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: 74051710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 112, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.12.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: 74051711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 112, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.12.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': True, '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: 74051712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 112, 'counter': 122, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.12.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': True, '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: 74051713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.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': True, '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: 74051714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 124, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 74051715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '112.36', 'subgroup_hash': 36, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051718
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '112.37', 'subgroup_hash': 37, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.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': '112.35', 'subgroup_hash': 35, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2.D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.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: 74051723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.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: 74051724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051726
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.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': '112.28', 'subgroup_hash': 28, 'subgroup_order': 112, 'subgroup_tex': 'C_4\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '112.29', 'subgroup_hash': 29, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74051730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051732
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '112.22', 'subgroup_hash': 22, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74051733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.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': '112.22', 'subgroup_hash': 22, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74051734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 74051735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 74051736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 74051737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 74051738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1.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': '112.27', 'subgroup_hash': 27, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 56, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.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': '112.23', 'subgroup_hash': 23, 'subgroup_order': 112, 'subgroup_tex': 'C_7\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.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': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.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': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.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': '112.5', 'subgroup_hash': 5, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.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': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.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': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 56, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.12.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.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': '112.7', 'subgroup_hash': 7, 'subgroup_order': 112, 'subgroup_tex': 'C_7:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 96, 'counter': 163, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '96.113', 'subgroup_hash': 113, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.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': '96.215', 'subgroup_hash': 215, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.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': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.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': '96.184', 'subgroup_hash': 184, 'subgroup_order': 96, 'subgroup_tex': 'Q_{16}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '96.158', 'subgroup_hash': 158, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.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': '96.149', 'subgroup_hash': 149, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.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': '96.116', 'subgroup_hash': 116, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74051765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '96.124', 'subgroup_hash': 124, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '96.124', 'subgroup_hash': 124, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '96.122', 'subgroup_hash': 122, 'subgroup_order': 96, 'subgroup_tex': 'C_8.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.122', 'subgroup_hash': 122, 'subgroup_order': 96, 'subgroup_tex': 'C_8.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '96.125', 'subgroup_hash': 125, 'subgroup_order': 96, 'subgroup_tex': 'Q_{16}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.14.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '96.125', 'subgroup_hash': 125, 'subgroup_order': 96, 'subgroup_tex': 'Q_{16}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 84, 'counter': 178, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.16.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: 74051774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 84, 'counter': 179, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 84, 'counter': 180, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': False, '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: 74051777
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 181, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', '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: 74051778
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 84, 'counter': 182, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.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: 74051779
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 84, 'counter': 183, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.f1.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': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051780
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 84, 'counter': 184, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.g1.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': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051781
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '84.14', 'subgroup_hash': 14, 'subgroup_order': 84, 'subgroup_tex': 'D_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74051783
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74051784
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74051785
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 42, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.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': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74051787
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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: 74051788
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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: 74051789
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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: 74051790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 42, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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: 74051791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 42, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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: 74051792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '84.8', 'subgroup_hash': 8, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74051793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 42, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.16.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '84.8', 'subgroup_hash': 8, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74051794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1344.8544.21.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': '64.255', 'subgroup_hash': 255, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 74051795
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 56, 'counter': 198, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.24.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: 74051796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 199, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.24.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': '24.14', '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': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 200, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.24.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': '24.14', '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': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 56, 'counter': 201, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.b1', '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': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.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': '56.3', 'subgroup_hash': 3, 'subgroup_order': 56, 'subgroup_tex': 'C_7:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051802
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 56, 'counter': 203, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.e1.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': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74051803
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 56, 'counter': 204, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.e1.b1', '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': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74051804
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051807
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.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: 74051811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051812
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 28, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.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': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 74051816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.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': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.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': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051821
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.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: 74051824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.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': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.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: 74051833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051834
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051835
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.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': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
  • id: 74051836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1.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: 74051840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.24.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1.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: 74051844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 48, 'counter': 241, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.28.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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 48, 'counter': 242, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': True, '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: 74051846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 48, 'counter': 243, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': True, '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: 74051847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 48, 'counter': 244, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.d1.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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 48, 'counter': 245, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.28.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.d1.b1', '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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 48, 'counter': 246, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.e1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.5', 'subgroup_hash': 5, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 48, 'counter': 247, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.28.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.e1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.5', 'subgroup_hash': 5, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.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': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.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': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051860
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74051865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 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: 74051867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 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: 74051868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 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: 74051869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 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': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 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: 74051871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 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: 74051872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.w1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.x1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.x1.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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.y1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.y1.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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.z1.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': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.ba1.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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.27', 'subgroup_hash': 27, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.bb1.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': '48.27', 'subgroup_hash': 27, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bc1.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': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.bd1.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': '48.18', 'subgroup_hash': 18, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.8', 'subgroup_hash': 8, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.28.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.be1.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': '48.8', 'subgroup_hash': 8, 'subgroup_order': 48, 'subgroup_tex': 'C_3:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051891
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 284, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.32.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': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'L2', 'C5'], '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: 74051892
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 42, 'counter': 285, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 74051893
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 42, 'counter': 286, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 74051894
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 21, 'counter': 287, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
  • id: 74051895
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 21, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.32.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': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
  • id: 74051896
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 21, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.32.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: 74051898
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 21, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '42.5', 'subgroup_hash': 5, 'subgroup_order': 42, 'subgroup_tex': 'D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 74051899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74051900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 16, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.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': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 16, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 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': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 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': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.42.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 306, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.48.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: 74051917
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 28, 'counter': 307, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.48.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': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', '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: 74051918
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 28, 'counter': 308, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.48.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': '48.38', '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: 74051919
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 14, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.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: 74051921
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.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: 74051923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74051924
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 14, 'counter': 313, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051925
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 314, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 74051926
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051927
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74051928
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051929
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 74051930
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 74051932
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 74051933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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: 74051934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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: 74051935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 7, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 74051936
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 7, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.48.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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: 74051937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 24, 'counter': 325, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.a1.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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 24, 'counter': 326, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.b1.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: 74051939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 327, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 24, 'counter': 328, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.d1.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 24, 'counter': 329, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.e1.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 330, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.f1.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 331, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.g1.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051945
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 24, 'counter': 332, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.56.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.h1.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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 74051946
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 24, 'counter': 333, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.56.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.h1.b1', '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': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 74051947
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 24, 'counter': 334, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.i1.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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051948
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 24, 'counter': 335, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.56.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.i1.b1', '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.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: 74051952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.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: 74051954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74051955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 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: 74051957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74051960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74051961
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.s1.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: 74051962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74051965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.w1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.x1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.y1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74051970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.ba1.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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bc1.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: 74051976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.be1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bg1.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: 74051981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74051983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.56.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.bi1.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: 74051984
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 21, 'counter': 368, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '1344.8544.64.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': '64.255', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 255, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'C6'], '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: 74051985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 16, 'counter': 369, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.84.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051988
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051989
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 74051993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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: 74051994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74051995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74051996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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: 74051998
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74051999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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: 74052001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 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: 74052002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052004
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 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: 74052007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 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: 74052009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 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: 74052010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 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: 74052011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.u1.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 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: 74052013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 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: 74052014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.w1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.x1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.x1.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.y1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.y1.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.z1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.z1.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.ba1.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bb1.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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bc1.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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.bd1.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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.84.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.be1.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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 74052034
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 412, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.96.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': '96.209', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 209, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], '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: 74052035
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 7, 'counter': 413, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.96.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: 74052036
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 7, 'counter': 414, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.96.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: 74052037
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 7, 'counter': 415, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.96.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74052038
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 7, 'counter': 416, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 74052039
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.96.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: 74052040
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 7, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 74052041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 419, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.112.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': '112.29', '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 224, 'characteristic': True, 'core_order': 12, 'counter': 420, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 12, 'counter': 421, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '112.c1.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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052045
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 422, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_{14}', '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: 74052046
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 12, 'counter': 423, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.e1.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: 74052047
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 12, 'counter': 424, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.112.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '112.f1.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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052048
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 12, 'counter': 425, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.112.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '112.g1.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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052051
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 428, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.112.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74052052
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 429, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.112.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74052054
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 430, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.112.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 74052055
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 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: 74052056
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 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: 74052057
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 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: 74052058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 6, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 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: 74052059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 6, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 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: 74052060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 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: 74052061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.112.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 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: 74052062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 8, 'counter': 438, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.168.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': ['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: 74052063
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 8, 'counter': 439, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052065
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 8, 'counter': 440, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.168.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1.b1', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74052067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052069
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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: 74052070
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052071
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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: 74052072
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 74052073
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052074
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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: 74052076
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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: 74052077
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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: 74052078
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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: 74052080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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: 74052081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052082
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.r1.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: 74052085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052088
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052090
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.w1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052091
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.x1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.y1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.z1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.z1.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: 74052095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bb1.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: 74052099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052100
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 472, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052101
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 473, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bd1.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 74052102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.be1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bg1.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: 74052106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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: 74052109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.168.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bi1.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: 74052110
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 7, 'counter': 481, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1344.8544.192.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': '192.1335', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1335, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:D_6', '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: 74052111
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 6, 'counter': 482, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.224.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': '224.176', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 176, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times 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: 74052112
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 224, 'characteristic': False, 'core_order': 6, 'counter': 483, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1344.8544.224.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '224.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.104', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 104, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052113
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 224, 'characteristic': False, 'core_order': 6, 'counter': 484, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1344.8544.224.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '224.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.104', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 104, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052114
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 3, 'counter': 485, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.224.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 74052115
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 3, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.224.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 74052116
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 487, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.224.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: 74052117
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.224.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 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: 74052118
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 489, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8544.336.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': '336.149', '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74052120
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 490, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.336.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': '336.219', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], '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: 74052121
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 491, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.336.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': '336.149', '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: 74052122
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 448, 'characteristic': False, 'core_order': 2, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.336.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: 74052123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.336.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: 74052124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.336.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: 74052125
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.336.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 74052126
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 496, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.336.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: 74052127
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 497, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.336.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: 74052128
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 498, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.336.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 74052129
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 499, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.336.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74052132
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 500, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.336.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: 74052133
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 501, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.336.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74052134
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 502, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.336.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74052135
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 503, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.336.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74052136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 1, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.336.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74052137
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 1, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.336.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74052138
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.336.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74052139
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.8544.336.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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: 74052140
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 3, 'counter': 508, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '1344.8544.448.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': '448.1200', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1200, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 448, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:D_{14}', '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: 74052141
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 509, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.8544.672.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': '672.1141', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1141, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times 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: 74052143
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 1, 'counter': 510, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.672.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: 74052144
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 448, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.672.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: 74052145
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 448, 'characteristic': False, 'core_order': 1, 'counter': 512, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.672.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 74052146
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.672.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: 74052147
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 514, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.672.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: 74052148
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 515, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.8544.672.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 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: 74052149
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.8544', 'ambient_counter': 8544, 'ambient_order': 1344, 'ambient_tex': 'C_{168}.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 1, 'counter': 516, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1344.8544.1344.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': '1344.8544', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8544, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{168}.C_2^3', '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: 74051686
    {'ambient': '1344.8544', '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', '2.h1.a1', '2.h1.b1', '2.i1.a1', '2.i1.b1', '2.j1.a1', '2.j1.b1', '2.k1.a1', '2.k1.b1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 448, 4, 672, 192, 2, 168], 'label': '1344.8544.1.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', '2.h1.a1', '2.h1.b1', '2.i1.a1', '2.i1.b1', '2.j1.a1', '2.j1.b1', '2.k1.a1', '2.k1.b1'], '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: 74051687
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '2.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.b1', '4.k1.a1', '4.p1.b1', '4.q1.b1', '4.r1.b1', '4.s1.b1', '6.h1.b1', '14.h1.b1'], 'core': '2.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 448, 168, 336, 4, 192, 672], 'label': '1344.8544.2.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.i1.b1', '4.k1.a1', '4.p1.b1', '4.q1.b1', '4.r1.b1', '4.s1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051688
    {'ambient': '1344.8544', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.x1.a1', '4.bb1.a1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.i1.a1', '16.o1.a1', '16.o1.b1', '24.l1.a1', '56.n1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2, 672, 448, 4, 192], 'label': '1344.8544.8.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.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: 74051689
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.l1.a1', '24.o1.a1', '56.o1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [205, 672, 448, 2, 192], 'label': '1344.8544.8.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74051690
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.b1.a1', '16.j1.b1', '16.l1.b1', '24.o1.b1', '56.o1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2, 672, 448, 204, 192], 'label': '1344.8544.8.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051691
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.x1.a1', '4.bb1.a1'], 'contains': ['16.b1.a1', '16.k1.a1', '16.m1.a1', '24.p1.a1', '56.p1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 672, 448, 2, 192], 'label': '1344.8544.8.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.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: 74051692
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.x1.a1', '4.bd1.a1'], 'contains': ['16.c1.a1', '16.h1.a1', '16.m1.a1', '24.q1.a1', '56.q1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [277, 672, 448, 6, 192], 'label': '1344.8544.8.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051693
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.x1.a1', '4.bd1.a1'], 'contains': ['16.c1.a1', '16.i1.a1', '16.k1.a1', '24.r1.a1', '56.r1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1235, 672, 448, 4, 192], 'label': '1344.8544.8.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051694
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.y1', '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.n1.a1', '4.y1.a1', '4.be1.a1'], 'contains': ['16.c1.a1', '16.j1.a1', '16.l1.b1', '24.u1.a1', '56.s1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1235, 672, 448, 204, 192], 'label': '1344.8544.8.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051695
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.y1', '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.n1.b1', '4.y1.a1', '4.be1.a1'], 'contains': ['16.c1.a1', '16.j1.b1', '16.l1.a1', '24.u1.b1', '56.s1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [477, 672, 448, 750, 192], 'label': '1344.8544.8.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051696
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.z1.a1', '4.bd1.a1'], 'contains': ['16.f1.a1', '16.h1.a1', '16.i1.a1', '24.v1.a1', '56.t1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [562, 672, 448, 4, 192], 'label': '1344.8544.8.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051697
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bb1.a1', '4.bd1.a1'], 'contains': ['16.e1.a1', '16.h1.a1', '16.k1.a1', '24.w1.a1', '56.u1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 448, 672, 6, 192], 'label': '1344.8544.8.ba1.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.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051698
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '2.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.f1.a1', '672.e1.a1', '672.b1.a1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.j1.a1', '4.k1.a1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1', '6.i1.a1', '14.i1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 448, 168, 1008, 2, 192, 672], 'label': '1344.8544.2.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.j1.a1', '4.k1.a1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051699
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.z1.a1', '4.bb1.a1'], 'contains': ['16.g1.a1', '16.h1.a1', '16.m1.a1', '24.x1.a1', '56.v1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 672, 448, 6, 192], 'label': '1344.8544.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051700
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bb1.a1', '4.bd1.a1'], 'contains': ['16.e1.a1', '16.i1.a1', '16.m1.a1', '24.y1.a1', '56.x1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 672, 448, 4, 192], 'label': '1344.8544.8.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051701
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.z1.a1', '4.bb1.a1'], 'contains': ['16.g1.a1', '16.i1.a1', '16.k1.a1', '24.z1.a1', '56.y1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 448, 4, 192], 'label': '1344.8544.8.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051702
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.be1', '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.d1.a1', '4.bc1.a1', '4.be1.a1'], 'contains': ['16.e1.a1', '16.j1.a1', '16.j1.b1', '24.be1.a1', '56.be1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 448, 672, 750, 192], 'label': '1344.8544.8.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051703
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bf1', '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.bc1.a1', '4.be1.a1'], 'contains': ['16.e1.a1', '16.l1.a1', '16.l1.b1', '24.bf1.a1', '56.bf1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 672, 448, 204, 192], 'label': '1344.8544.8.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051704
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bg1', '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', '4.ba1.a1', '4.be1.a1'], 'contains': ['16.f1.a1', '16.j1.a1', '16.l1.a1', '24.bg1.a1', '56.bg1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [205, 672, 448, 562, 192], 'label': '1344.8544.8.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051705
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bg1', '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', '4.ba1.a1', '4.be1.a1'], 'contains': ['16.f1.a1', '16.j1.b1', '16.l1.b1', '24.bg1.b1', '56.bg1.b1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [562, 672, 448, 204, 192], 'label': '1344.8544.8.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051706
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.z1.a1', '4.bd1.a1'], 'contains': ['16.f1.a1', '16.k1.a1', '16.m1.a1', '24.bh1.a1', '56.bh1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 672, 448, 562, 192], 'label': '1344.8544.8.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051707
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bi1', '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.n1.a1', '4.ba1.a1', '4.bc1.a1'], 'contains': ['16.g1.a1', '16.j1.a1', '16.l1.b1', '24.bi1.a1', '56.bi1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3, 672, 448, 204, 192], 'label': '1344.8544.8.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051708
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '8.bi1', '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.n1.b1', '4.ba1.a1', '4.bc1.a1'], 'contains': ['16.g1.a1', '16.j1.b1', '16.l1.a1', '24.bi1.b1', '56.bi1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [205, 672, 448, 750, 192], 'label': '1344.8544.8.bi1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051709
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '2.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.f1.a1', '672.e1.a1', '672.b1.a1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.b1', '4.j1.a1', '4.k1.b1', '4.t1.b1', '4.u1.b1', '4.v1.b1', '4.w1.b1', '6.i1.b1', '14.i1.b1'], 'core': '2.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 204, 336, 2, 192, 672], 'label': '1344.8544.2.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.b1', '4.j1.a1', '4.k1.b1', '4.t1.b1', '4.u1.b1', '4.v1.b1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051710
    {'ambient': '1344.8544', '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': '56.e1.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.d1.a1', '24.g1.a1', '24.w1.a1', '84.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 672, 6, 192], 'label': '1344.8544.12.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.d1.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: 74051711
    {'ambient': '1344.8544', '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': '56.a1.a1', 'complements': ['112.o1.a1', '112.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1', '24.j1.a1', '24.be1.a1', '84.h1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 672, 750, 192], 'label': '1344.8544.12.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.c1.b1'], '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: 74051712
    {'ambient': '1344.8544', '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': '8.d1.a1', 'complements': ['112.o1.a1', '112.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.e1.b1', '84.a1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 168, 672], 'label': '1344.8544.12.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', '24.e1.a1', '24.e1.b1', '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: 74051713
    {'ambient': '1344.8544', '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': '112.b1.a1', 'complements': ['112.n1.a1', '112.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.a1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.e1.b1', '84.x1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 336, 672, 6, 192], 'label': '1344.8544.12.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.p1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.c1.a1', '24.e1.b1'], 'normalizer': '1.a1.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: 74051714
    {'ambient': '1344.8544', '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': '112.b1.a1', 'complements': ['112.n1.a1', '112.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '6.a1.a1', '6.h1.b1', '6.j1.b1'], 'contains': ['24.b1.a1', '24.c1.b1', '24.e1.a1', '84.x1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 336, 672, 168, 192], 'label': '1344.8544.12.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.p1.b1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.c1.b1', '24.e1.a1'], 'normalizer': '1.a1.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: 74051715
    {'ambient': '1344.8544', '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': '112.b1.a1', 'complements': ['112.o1.a1', '112.o1.b1', '112.n1.a1', '112.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.a1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.e1.a1', '84.bb1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 1008, 672, 168, 192], 'label': '1344.8544.12.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.t1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.d1.a1', '24.e1.a1'], 'normalizer': '1.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: 74051716
    {'ambient': '1344.8544', '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': '112.b1.a1', 'complements': ['112.o1.a1', '112.o1.b1', '112.n1.a1', '112.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.t1.b1', '6.a1.a1', '6.i1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.d1.a1', '24.e1.b1', '84.bb1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 336, 672, 750, 192], 'label': '1344.8544.12.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': ['4.t1.b1', '6.a1.a1'], 'normal_contains': ['24.c1.b1', '24.d1.a1', '24.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051717
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '6.b1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.h1.a1', '24.l1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1', '84.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 4, 672, 2, 192], 'label': '1344.8544.12.f1.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.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: 74051718
    {'ambient': '1344.8544', '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.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.i1.a1', '24.m1.a1', '24.n1.a1', '24.s1.a1', '24.t1.a1', '84.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 336, 192, 2, 672], 'label': '1344.8544.12.g1.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.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: 74051719
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '6.c1.a1'], 'contains': ['24.f1.a1', '24.j1.a1', '24.k1.a1', '24.o1.a1', '24.o1.b1', '24.u1.a1', '24.u1.b1', '84.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 204, 672, 898, 192], 'label': '1344.8544.12.h1.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.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: 74051720
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '2.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.f1.a1', '672.c1.a1', '672.c1.b1', '672.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.a1', '4.n1.a1', '4.o1.b1', '4.p1.a1', '4.q1.b1', '4.u1.a1', '4.w1.b1', '6.j1.a1', '14.j1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 204, 336, 58, 192, 672], 'label': '1344.8544.2.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.a1', '4.n1.a1', '4.o1.b1', '4.p1.a1', '4.q1.b1', '4.u1.a1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051721
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '6.b1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.i1.a1', '24.v1.a1', '24.x1.a1', '24.z1.a1', '24.bh1.a1', '84.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 4, 672, 1010, 192], 'label': '1344.8544.12.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': '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: 74051722
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '24.y1.a1', '24.ba1.a1', '24.bc1.a1', '84.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 336, 672, 4, 192], 'label': '1344.8544.12.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051723
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.k1.a1', '24.bb1.a1', '24.bb1.b1', '24.bf1.a1', '84.i1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 336, 672, 204, 192], 'label': '1344.8544.12.k1.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.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: 74051724
    {'ambient': '1344.8544', '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': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.bd1.a1', '24.bd1.b1', '84.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 1008, 58, 672], 'label': '1344.8544.12.l1.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.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: 74051725
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '6.c1.a1'], 'contains': ['24.i1.a1', '24.j1.a1', '24.k1.a1', '24.bg1.a1', '24.bg1.b1', '24.bi1.a1', '24.bi1.b1', '84.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 204, 672, 562, 192], 'label': '1344.8544.12.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: 74051726
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '6.b1.a1'], 'contains': ['24.l1.a1', '24.n1.a1', '24.p1.a1', '24.w1.a1', '24.x1.a1', '24.y1.a1', '24.z1.a1', '84.l1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 4, 672, 2, 192], 'label': '1344.8544.12.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: 74051727
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1', '6.h1.a1', '6.h1.b1'], 'contains': ['24.b1.a1', '24.l1.a1', '24.m1.a1', '24.v1.a1', '24.ba1.a1', '84.m1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 336, 672, 4, 192], 'label': '1344.8544.12.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051728
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.c1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.c1.a1', '24.m1.a1', '24.o1.a1', '24.bb1.a1', '24.bg1.a1', '84.n1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [653, 336, 672, 2, 192], 'label': '1344.8544.12.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051729
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.c1.a1', '6.h1.b1', '6.i1.b1'], 'contains': ['24.c1.b1', '24.m1.a1', '24.o1.b1', '24.bb1.b1', '24.bg1.b1', '84.n1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [898, 336, 672, 204, 192], 'label': '1344.8544.12.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051730
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.b1.a1', '6.i1.a1', '6.i1.b1'], 'contains': ['24.d1.a1', '24.m1.a1', '24.p1.a1', '24.bc1.a1', '24.bh1.a1', '84.o1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 336, 672, 2, 192], 'label': '1344.8544.12.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051731
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '2.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.f1.a1', '672.c1.a1', '672.c1.b1', '672.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.a1', '4.n1.b1', '4.o1.a1', '4.p1.b1', '4.q1.a1', '4.u1.b1', '4.w1.a1', '6.j1.b1', '14.j1.b1'], 'core': '2.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 448, 168, 1008, 6, 192, 672], 'label': '1344.8544.2.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.a1', '4.n1.b1', '4.o1.a1', '4.p1.b1', '4.q1.a1', '4.u1.b1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051732
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.d1.a1', '6.h1.b1', '6.i1.a1'], 'contains': ['24.e1.a1', '24.m1.a1', '24.bd1.a1', '84.p1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 336, 168, 672], 'label': '1344.8544.12.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051733
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.b1', '6.d1.a1', '6.h1.a1', '6.i1.b1'], 'contains': ['24.e1.b1', '24.m1.a1', '24.bd1.b1', '84.p1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 336, 2, 672], 'label': '1344.8544.12.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051734
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.s1', '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': ['4.bc1.a1', '6.c1.a1'], 'contains': ['24.n1.a1', '24.o1.a1', '24.o1.b1', '24.be1.a1', '24.bf1.a1', '24.bi1.a1', '24.bi1.b1', '84.q1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 204, 672, 898, 192], 'label': '1344.8544.12.s1.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.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051735
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '6.b1.a1'], 'contains': ['24.q1.a1', '24.r1.a1', '24.t1.a1', '24.v1.a1', '24.w1.a1', '24.y1.a1', '24.bh1.a1', '84.r1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 4, 672, 1010, 192], 'label': '1344.8544.12.t1.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.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051736
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.b1.a1', '6.j1.a1', '6.j1.b1'], 'contains': ['24.b1.a1', '24.q1.a1', '24.s1.a1', '24.x1.a1', '24.bc1.a1', '84.s1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 336, 672, 6, 192], 'label': '1344.8544.12.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051737
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.b1.a1', '6.k1.a1', '6.k1.b1'], 'contains': ['24.d1.a1', '24.r1.a1', '24.s1.a1', '24.z1.a1', '24.ba1.a1', '84.t1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 336, 672, 4, 192], 'label': '1344.8544.12.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051738
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.w1', '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': ['4.n1.a1', '6.c1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.s1.a1', '24.u1.a1', '24.bb1.b1', '24.bi1.a1', '84.u1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [899, 336, 672, 204, 192], 'label': '1344.8544.12.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051739
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.w1', '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': ['4.n1.b1', '6.c1.a1', '6.j1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.s1.a1', '24.u1.b1', '24.bb1.a1', '24.bi1.b1', '84.u1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [205, 336, 672, 750, 192], 'label': '1344.8544.12.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051740
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.d1.a1', '6.j1.b1', '6.k1.a1'], 'contains': ['24.e1.a1', '24.s1.a1', '24.bd1.b1', '84.v1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 192, 336, 168, 672], 'label': '1344.8544.12.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051741
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '6.d1.a1', '6.j1.a1', '6.k1.b1'], 'contains': ['24.e1.b1', '24.s1.a1', '24.bd1.a1', '84.v1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 336, 58, 672], 'label': '1344.8544.12.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051742
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '2.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.c1.a1', '672.c1.b1', '672.e1.a1', '672.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.m1.a1', '4.n1.a1', '4.o1.a1', '4.r1.a1', '4.s1.b1', '4.t1.a1', '4.v1.b1', '6.k1.a1', '14.k1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 448, 168, 336, 4, 192, 672], 'label': '1344.8544.2.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.m1.a1', '4.n1.a1', '4.o1.a1', '4.r1.a1', '4.s1.b1', '4.t1.a1', '4.v1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051743
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.y1', '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': ['4.be1.a1', '6.c1.a1'], 'contains': ['24.t1.a1', '24.u1.a1', '24.u1.b1', '24.be1.a1', '24.bf1.a1', '24.bg1.a1', '24.bg1.b1', '84.w1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 204, 672, 562, 192], 'label': '1344.8544.12.y1.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.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051744
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.z1', '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.q1.a1', '6.e1.a1', '6.h1.a1', '6.j1.b1'], 'contains': ['24.b1.a1', '24.bb1.a1', '24.bd1.b1', '84.y1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [205, 336, 672, 6, 192], 'label': '1344.8544.12.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051745
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.z1', '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.q1.b1', '6.e1.a1', '6.h1.b1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.bb1.b1', '24.bd1.a1', '84.y1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [58, 1008, 672, 204, 192], 'label': '1344.8544.12.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051746
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.ba1', '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.r1.a1', '6.f1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.ba1.a1', '24.bd1.b1', '84.z1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [507, 1008, 672, 4, 192], 'label': '1344.8544.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051747
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.ba1', '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.r1.b1', '6.f1.a1', '6.h1.b1', '6.k1.b1'], 'contains': ['24.c1.b1', '24.ba1.a1', '24.bd1.a1', '84.z1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [506, 1008, 672, 4, 192], 'label': '1344.8544.12.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051748
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.bb1', '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.s1.a1', '6.g1.a1', '6.h1.a1', '6.k1.b1'], 'contains': ['24.e1.b1', '24.ba1.a1', '24.bb1.a1', '84.ba1.a1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 336, 672, 4, 192], 'label': '1344.8544.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051749
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.bb1', '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.s1.b1', '6.g1.a1', '6.h1.b1', '6.k1.a1'], 'contains': ['24.e1.a1', '24.ba1.a1', '24.bb1.b1', '84.ba1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [4, 336, 672, 168, 192], 'label': '1344.8544.12.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051750
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.bc1', '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.u1.a1', '6.f1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.c1.a1', '24.bc1.a1', '24.bd1.a1', '84.bc1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [901, 336, 672, 58, 192], 'label': '1344.8544.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051751
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.bc1', '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.u1.b1', '6.f1.a1', '6.i1.b1', '6.j1.b1'], 'contains': ['24.c1.b1', '24.bc1.a1', '24.bd1.b1', '84.bc1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 336, 672, 750, 192], 'label': '1344.8544.12.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051752
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.bd1', '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.v1.a1', '6.e1.a1', '6.i1.a1', '6.k1.b1'], 'contains': ['24.d1.a1', '24.bb1.a1', '24.bd1.a1', '84.bd1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [205, 336, 672, 58, 192], 'label': '1344.8544.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051753
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '2.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.c1.a1', '672.c1.b1', '672.e1.a1', '672.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.m1.a1', '4.n1.b1', '4.o1.b1', '4.r1.b1', '4.s1.a1', '4.t1.b1', '4.v1.a1', '6.k1.b1', '14.k1.b1'], 'core': '2.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 4, 336, 58, 192, 672], 'label': '1344.8544.2.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.m1.a1', '4.n1.b1', '4.o1.b1', '4.r1.b1', '4.s1.a1', '4.t1.b1', '4.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051754
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.bd1', '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.v1.b1', '6.e1.a1', '6.i1.b1', '6.k1.a1'], 'contains': ['24.d1.a1', '24.bb1.b1', '24.bd1.b1', '84.bd1.b1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [59, 1008, 672, 204, 192], 'label': '1344.8544.12.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051755
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.be1', '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.w1.a1', '6.g1.a1', '6.i1.a1', '6.j1.b1'], 'contains': ['24.e1.a1', '24.bb1.a1', '24.bc1.a1', '84.be1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 1008, 672, 168, 192], 'label': '1344.8544.12.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051756
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '12.be1', '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.w1.b1', '6.g1.a1', '6.i1.b1', '6.j1.a1'], 'contains': ['24.e1.b1', '24.bb1.b1', '24.bc1.a1', '84.be1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 336, 672, 204, 192], 'label': '1344.8544.12.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051757
    {'ambient': '1344.8544', '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.b1.a1', 'complements': ['96.f1.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', '28.d1.a1', '28.d1.b1', '28.e1.a1', '28.e1.b1', '42.c1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 672, 2, 168, 336], 'label': '1344.8544.14.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', '28.d1.a1', '28.d1.b1', '28.e1.a1', '28.e1.b1'], '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: 74051758
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.f1.a1', '28.h1.a1', '28.i1.a1', '28.j1.a1', '28.n1.a1', '28.o1.a1', '28.q1.a1', '28.s1.a1', '28.t1.a1', '28.u1.a1', '42.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 2, 4, 336], 'label': '1344.8544.14.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: 74051759
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.g1.a1', '28.k1.a1', '28.l1.a1', '28.m1.a1', '28.p1.a1', '28.p1.b1', '28.r1.a1', '28.v1.a1', '28.v1.b1', '28.w1.a1', '42.b1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 2, 204, 336], 'label': '1344.8544.14.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: 74051760
    {'ambient': '1344.8544', '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.b1.a1', '28.i1.a1', '28.k1.a1', '28.x1.a1', '28.x1.b1', '28.bb1.a1', '28.bb1.b1', '42.d1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 336, 6, 168, 448], 'label': '1344.8544.14.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: 74051761
    {'ambient': '1344.8544', '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': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.i1.a1', '28.l1.a1', '28.y1.a1', '28.y1.b1', '28.bd1.a1', '28.bd1.b1', '42.e1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 58, 204, 1008], 'label': '1344.8544.14.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: 74051762
    {'ambient': '1344.8544', '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': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.j1.a1', '28.k1.a1', '28.z1.a1', '28.z1.b1', '28.bc1.a1', '28.bc1.b1', '42.f1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 58, 4, 1008], 'label': '1344.8544.14.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: 74051763
    {'ambient': '1344.8544', '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.b1.a1', '28.j1.a1', '28.l1.a1', '28.ba1.a1', '28.ba1.b1', '28.be1.a1', '28.be1.b1', '42.g1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 672, 4, 168, 336], 'label': '1344.8544.14.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: 74051764
    {'ambient': '1344.8544', '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': '336.d1.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', '6.h1.a1', '6.h1.b1', '6.i1.a1', '6.i1.b1', '6.j1.a1', '6.j1.b1', '6.k1.a1', '6.k1.b1', '21.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 672, 4, 168, 2, 192, 336], 'label': '1344.8544.3.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: 74051765
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '14.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.h1.a1', '7.a1.a1'], 'contains': ['28.d1.b1', '28.o1.a1', '28.p1.a1', '28.x1.a1', '28.y1.a1', '28.z1.a1', '28.ba1.a1', '42.h1.a1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 672, 2, 4, 336], 'label': '1344.8544.14.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051766
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '14.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.h1.b1', '7.a1.a1'], 'contains': ['28.d1.a1', '28.o1.a1', '28.p1.b1', '28.x1.b1', '28.y1.b1', '28.z1.b1', '28.ba1.b1', '42.h1.b1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2, 448, 672, 4, 168, 336], 'label': '1344.8544.14.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051767
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '14.i1', '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.i1.a1', '7.a1.a1'], 'contains': ['28.d1.a1', '28.p1.a1', '28.q1.a1', '28.bb1.a1', '28.bc1.a1', '28.bd1.a1', '28.be1.a1', '42.i1.a1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 672, 2, 168, 1008], 'label': '1344.8544.14.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051768
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '14.i1', '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.i1.b1', '7.a1.a1'], 'contains': ['28.d1.b1', '28.p1.b1', '28.q1.a1', '28.bb1.b1', '28.bc1.b1', '28.bd1.b1', '28.be1.b1', '42.i1.b1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 672, 2, 204, 336], 'label': '1344.8544.14.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051769
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '14.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.j1.a1', '7.a1.a1'], 'contains': ['28.e1.b1', '28.t1.a1', '28.v1.a1', '28.x1.a1', '28.y1.b1', '28.bc1.a1', '28.be1.b1', '42.j1.a1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 672, 58, 204, 336], 'label': '1344.8544.14.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051770
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '14.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.j1.b1', '7.a1.a1'], 'contains': ['28.e1.a1', '28.t1.a1', '28.v1.b1', '28.x1.b1', '28.y1.a1', '28.bc1.b1', '28.be1.a1', '42.j1.b1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 672, 6, 168, 1008], 'label': '1344.8544.14.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051771
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '14.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.k1.a1', '7.a1.a1'], 'contains': ['28.e1.a1', '28.u1.a1', '28.v1.a1', '28.z1.a1', '28.ba1.b1', '28.bb1.a1', '28.bd1.b1', '42.k1.a1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 448, 672, 4, 168, 336], 'label': '1344.8544.14.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051772
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '14.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.k1.b1', '7.a1.a1'], 'contains': ['28.e1.b1', '28.u1.a1', '28.v1.b1', '28.z1.b1', '28.ba1.a1', '28.bb1.b1', '28.bd1.a1', '42.k1.b1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 672, 58, 4, 336], 'label': '1344.8544.14.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051773
    {'ambient': '1344.8544', '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.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.p1.a1', '8.q1.a1', '8.r1.a1', '8.s1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '48.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [337, 448, 192, 672], 'label': '1344.8544.16.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], '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: 74051774
    {'ambient': '1344.8544', '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': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.t1.a1', '8.u1.a1', '8.u1.b1', '8.v1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '48.d1.a1', '112.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 448, 672], 'label': '1344.8544.16.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.e1.a1', '8.d1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.b1', '32.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: 74051775
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '12.g1.a1', '28.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 336, 192, 2, 672], 'label': '1344.8544.4.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.b1.a1', '8.c1.a1', '8.e1.a1', '8.d1.a1', '8.g1.a1', '8.f1.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: 74051776
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '8.w1.a1', '8.x1.a1', '8.y1.a1', '8.y1.b1'], 'contains': ['32.a1.a1', '32.d1.a1', '48.e1.a1', '112.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1235, 192, 448, 672], 'label': '1344.8544.16.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.g1.a1', '8.f1.a1'], 'normal_contains': ['32.a1.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: 74051777
    {'ambient': '1344.8544', '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': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.j1.b1', '8.k1.a1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.n1.a1', '8.n1.b1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '48.b1.a1', '112.d1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 192, 672, 448], 'label': '1344.8544.16.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.j1.b1', '8.k1.a1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.n1.a1', '8.n1.b1', '8.o1.b1', '8.o1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1', '112.d1.a1'], 'normalizer': '1.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: 74051778
    {'ambient': '1344.8544', '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': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.e1.a1', '8.g1.a1', '8.ba1.a1', '8.bc1.a1', '8.be1.a1', '8.bf1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '112.e1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 672, 448], 'label': '1344.8544.16.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.b1.a1', '8.e1.a1', '8.g1.a1'], 'normal_contains': ['32.a1.a1', '48.c1.a1', '112.e1.a1'], 'normalizer': '1.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: 74051779
    {'ambient': '1344.8544', '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': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.d1.a1', '8.g1.a1', '8.z1.a1', '8.bg1.a1', '8.bg1.b1', '8.bh1.a1'], 'contains': ['32.a1.a1', '48.h1.a1', '112.f1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [562, 672, 448, 192], 'label': '1344.8544.16.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.c1.a1', '8.d1.a1', '8.g1.a1'], 'normal_contains': ['32.a1.a1', '112.f1.a1'], 'normalizer': '1.a1.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: 74051780
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.a1', '8.f1.a1', '8.bb1.a1', '8.bd1.a1', '8.bi1.a1', '8.bi1.b1'], 'contains': ['32.a1.a1', '48.i1.a1', '112.g1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 672, 448, 192], 'label': '1344.8544.16.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.c1.a1', '8.e1.a1', '8.f1.a1'], 'normal_contains': ['32.a1.a1', '112.g1.a1'], 'normalizer': '1.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: 74051781
    {'ambient': '1344.8544', '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.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.p1.a1', '8.t1.a1', '8.w1.a1', '8.z1.a1', '8.ba1.a1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '48.f1.a1', '112.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 448, 192, 672], 'label': '1344.8544.16.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.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: 74051782
    {'ambient': '1344.8544', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.q1.a1', '8.t1.a1', '8.x1.a1', '8.z1.a1', '8.bc1.a1', '8.bd1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '48.g1.a1', '112.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [4, 448, 192, 672], 'label': '1344.8544.16.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.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: 74051783
    {'ambient': '1344.8544', '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.j1.a1', '8.r1.a1', '8.u1.a1', '8.y1.a1', '8.be1.a1', '8.bg1.a1', '8.bi1.a1'], 'contains': ['32.a1.a1', '48.j1.a1', '112.j1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [751, 672, 192, 448], 'label': '1344.8544.16.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74051784
    {'ambient': '1344.8544', '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.j1.b1', '8.r1.a1', '8.u1.b1', '8.y1.b1', '8.be1.a1', '8.bg1.b1', '8.bi1.b1'], 'contains': ['32.a1.a1', '48.j1.b1', '112.j1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [750, 672, 192, 448], 'label': '1344.8544.16.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051785
    {'ambient': '1344.8544', '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': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.p1.a1', '8.v1.a1', '8.x1.a1', '8.ba1.a1', '8.bd1.a1', '8.bh1.a1'], 'contains': ['32.a1.a1', '48.k1.a1', '112.k1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [7, 672, 192, 448], 'label': '1344.8544.16.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.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: 74051786
    {'ambient': '1344.8544', '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.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.k1.a1', '8.p1.a1', '8.ba1.a1', '12.a1.a1', '28.i1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 448, 6, 672], 'label': '1344.8544.4.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.b1.a1', '8.h1.a1', '8.k1.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: 74051787
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '16.l1', '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.l1.a1', '8.s1.a1', '8.u1.a1', '8.y1.b1', '8.bf1.a1', '8.bg1.a1', '8.bi1.b1'], 'contains': ['32.a1.a1', '48.l1.a1', '112.l1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [205, 448, 192, 672], 'label': '1344.8544.16.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051788
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '16.l1', '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.l1.b1', '8.s1.a1', '8.u1.b1', '8.y1.a1', '8.bf1.a1', '8.bg1.b1', '8.bi1.a1'], 'contains': ['32.a1.a1', '48.l1.b1', '112.l1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [204, 448, 192, 672], 'label': '1344.8544.16.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051789
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.q1.a1', '8.v1.a1', '8.w1.a1', '8.bb1.a1', '8.bc1.a1', '8.bh1.a1'], 'contains': ['32.a1.a1', '48.m1.a1', '112.m1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [5, 448, 192, 672], 'label': '1344.8544.16.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051790
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '16.n1', '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.a1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.d1.a1', '48.n1.a1', '112.n1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 192, 448, 2], 'label': '1344.8544.16.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051791
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '16.n1', '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.a1.a1'], 'contains': ['32.b1.b1', '32.c1.a1', '32.d1.a1', '48.n1.b1', '112.n1.b1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 192, 448, 226], 'label': '1344.8544.16.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051792
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '32.f1.a1', '48.o1.a1', '112.o1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2, 448, 192, 4], 'label': '1344.8544.16.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051793
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1'], 'contains': ['32.b1.b1', '32.e1.a1', '32.f1.a1', '48.o1.b1', '112.o1.b1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [226, 448, 192, 4], 'label': '1344.8544.16.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051794
    {'ambient': '1344.8544', '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': '336.d1.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', '42.h1.a1', '42.h1.b1', '42.i1.a1', '42.i1.b1', '42.j1.a1', '42.j1.b1', '42.k1.a1', '42.k1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 2, 4, 168], 'label': '1344.8544.21.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: 74051795
    {'ambient': '1344.8544', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.g1.a1', '12.j1.a1', '12.k1.a1', '12.l1.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': [1, 192, 672, 336], 'label': '1344.8544.24.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.b1.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: 74051796
    {'ambient': '1344.8544', '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.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.a1.a1', '12.d1.a1', '12.d1.b1', '12.o1.a1', '12.u1.a1', '12.z1.a1', '12.z1.b1'], 'contains': ['48.b1.a1', '48.f1.a1', '168.v1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 672, 192, 336], 'label': '1344.8544.24.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.h1.a1', '12.a1.a1', '12.d1.a1', '12.d1.b1'], 'normal_contains': ['48.b1.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: 74051797
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.h1.a1', '4.j1.a1', '4.l1.a1', '4.m1.a1', '4.x1.a1', '4.z1.a1', '4.bb1.a1', '4.bd1.a1', '6.b1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 4, 336, 2, 192, 672], 'label': '1344.8544.2.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.c1.a1', '4.h1.a1', '4.j1.a1', '4.l1.a1', '4.m1.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: 74051798
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.i1.a1', '8.m1.a1', '8.q1.a1', '8.bc1.a1', '12.j1.a1', '28.j1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 672, 4, 448], 'label': '1344.8544.4.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.i1.a1', '8.m1.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: 74051799
    {'ambient': '1344.8544', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.b1.a1', '12.d1.a1', '12.e1.a1', '12.p1.a1', '12.w1.a1', '12.ba1.a1', '12.bc1.a1'], 'contains': ['48.b1.a1', '48.j1.a1', '168.z1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [751, 672, 192, 336], 'label': '1344.8544.24.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.j1.a1', '12.b1.a1', '12.d1.a1', '12.e1.a1'], 'normal_contains': ['48.b1.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: 74051800
    {'ambient': '1344.8544', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '12.b1.a1', '12.d1.b1', '12.e1.b1', '12.p1.b1', '12.w1.b1', '12.ba1.b1', '12.bc1.b1'], 'contains': ['48.b1.a1', '48.j1.b1', '168.z1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [750, 672, 192, 336], 'label': '1344.8544.24.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': ['8.j1.b1', '12.b1.a1', '12.d1.b1', '12.e1.b1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051801
    {'ambient': '1344.8544', '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': '56.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.a1.a1', '12.e1.a1', '12.e1.b1', '12.q1.a1', '12.v1.a1', '12.bd1.a1', '12.bd1.b1'], 'contains': ['48.b1.a1', '48.k1.a1', '168.ba1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 672, 192, 336], 'label': '1344.8544.24.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.k1.a1', '12.a1.a1', '12.e1.a1', '12.e1.b1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.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: 74051802
    {'ambient': '1344.8544', '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': '4.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.c1.a1', '12.d1.b1', '12.e1.a1', '12.r1.a1', '12.x1.a1', '12.bb1.b1', '12.be1.a1'], 'contains': ['48.b1.a1', '168.b1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168, 336, 672, 192], 'label': '1344.8544.24.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.n1.a1', '12.c1.a1', '12.d1.b1', '12.e1.a1'], 'normal_contains': ['48.b1.a1', '168.b1.a1'], 'normalizer': '1.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: 74051803
    {'ambient': '1344.8544', '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': '4.k1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '12.c1.a1', '12.d1.a1', '12.e1.b1', '12.r1.b1', '12.x1.b1', '12.bb1.a1', '12.be1.b1'], 'contains': ['48.b1.a1', '168.b1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 336, 672, 192], 'label': '1344.8544.24.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.b1', 'normal_contained_in': ['8.n1.b1', '12.c1.a1', '12.d1.a1', '12.e1.b1'], 'normal_contains': ['48.b1.a1', '168.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051804
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.e1.a1', '48.n1.a1', '48.n1.b1', '168.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [337, 672, 192, 2], 'label': '1344.8544.24.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051805
    {'ambient': '1344.8544', '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': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.a1.a1', '12.f1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.k1.a1', '168.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 672, 192, 6], 'label': '1344.8544.24.g1.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.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: 74051806
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.f1.a1', '12.i1.a1', '12.j1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '48.m1.a1', '168.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 672, 192, 4], 'label': '1344.8544.24.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.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: 74051807
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.g1.a1', '12.i1.a1', '12.m1.a1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.i1.a1', '168.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [337, 192, 672, 562], 'label': '1344.8544.24.i1.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.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: 74051808
    {'ambient': '1344.8544', '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': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '12.b1.a1', '12.h1.a1', '12.m1.a1'], 'contains': ['48.a1.a1', '48.j1.a1', '48.j1.b1', '168.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 672, 192, 750], 'label': '1344.8544.24.j1.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.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: 74051809
    {'ambient': '1344.8544', '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': '112.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '8.j1.b1', '8.r1.a1', '8.be1.a1', '12.b1.a1', '28.k1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 448, 750, 672], 'label': '1344.8544.4.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '8.j1.a1', '8.j1.b1', '12.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: 74051810
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '12.h1.a1', '12.k1.a1', '12.m1.a1'], 'contains': ['48.a1.a1', '48.l1.a1', '48.l1.b1', '168.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 672, 192, 204], 'label': '1344.8544.24.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.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: 74051811
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '12.f1.a1', '12.n1.a1', '12.o1.a1'], 'contains': ['48.d1.a1', '48.f1.a1', '48.g1.a1', '48.o1.a1', '48.o1.b1', '168.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2, 672, 192, 4], 'label': '1344.8544.24.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.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: 74051812
    {'ambient': '1344.8544', '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': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.g1.a1', '12.o1.a1', '12.p1.a1', '12.p1.b1', '12.q1.a1', '12.r1.a1', '12.r1.b1'], 'contains': ['48.b1.a1', '48.d1.a1', '48.h1.a1', '168.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 672, 336], 'label': '1344.8544.24.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.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: 74051813
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.g1.a1', '12.n1.a1', '12.s1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.i1.a1', '168.k1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 672, 2], 'label': '1344.8544.24.n1.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.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: 74051814
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '12.h1.a1', '12.p1.a1', '12.s1.a1'], 'contains': ['48.d1.a1', '48.j1.a1', '48.l1.a1', '168.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [653, 672, 192, 2], 'label': '1344.8544.24.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.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: 74051815
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.b1', '12.h1.a1', '12.p1.b1', '12.s1.a1'], 'contains': ['48.d1.a1', '48.j1.b1', '48.l1.b1', '168.l1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [898, 672, 192, 204], 'label': '1344.8544.24.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051816
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '12.f1.a1', '12.n1.a1', '12.q1.a1'], 'contains': ['48.d1.a1', '48.k1.a1', '48.m1.a1', '168.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5, 672, 192, 2], 'label': '1344.8544.24.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.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: 74051817
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '12.f1.a1', '12.t1.a1', '12.u1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.m1.a1', '168.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [277, 672, 192, 6], 'label': '1344.8544.24.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.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: 74051818
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '12.f1.a1', '12.t1.a1', '12.v1.a1'], 'contains': ['48.e1.a1', '48.g1.a1', '48.k1.a1', '168.o1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [339, 672, 192, 4], 'label': '1344.8544.24.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.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: 74051819
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.g1.a1', '12.u1.a1', '12.v1.a1', '12.w1.a1', '12.w1.b1', '12.x1.a1', '12.x1.b1'], 'contains': ['48.b1.a1', '48.e1.a1', '48.i1.a1', '168.p1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 192, 672, 336], 'label': '1344.8544.24.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051820
    {'ambient': '1344.8544', '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': ['336.o1.a1', '336.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.l1.a1', '8.l1.b1', '8.s1.a1', '8.bf1.a1', '12.k1.a1', '28.l1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 336, 672, 204, 448], 'label': '1344.8544.4.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.l1.a1', '8.l1.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: 74051821
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.g1.a1', '12.t1.a1', '12.y1.a1'], 'contains': ['48.c1.a1', '48.e1.a1', '48.h1.a1', '168.q1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 672, 562], 'label': '1344.8544.24.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051822
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '12.h1.a1', '12.w1.a1', '12.y1.a1'], 'contains': ['48.e1.a1', '48.j1.a1', '48.l1.b1', '168.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1235, 672, 192, 204], 'label': '1344.8544.24.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.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: 74051823
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.b1', '12.h1.a1', '12.w1.b1', '12.y1.a1'], 'contains': ['48.e1.a1', '48.j1.b1', '48.l1.a1', '168.r1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [477, 672, 192, 750], 'label': '1344.8544.24.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051824
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '12.i1.a1', '12.o1.a1', '12.t1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '48.h1.a1', '168.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1010, 672, 192, 4], 'label': '1344.8544.24.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.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: 74051825
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '12.a1.a1', '12.n1.a1', '12.t1.a1'], 'contains': ['48.c1.a1', '48.f1.a1', '48.k1.a1', '168.t1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 672, 192, 6], 'label': '1344.8544.24.w1.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.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051826
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '12.i1.a1', '12.n1.a1', '12.u1.a1'], 'contains': ['48.f1.a1', '48.i1.a1', '48.m1.a1', '168.u1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5, 672, 192, 6], 'label': '1344.8544.24.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051827
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '12.j1.a1', '12.n1.a1', '12.t1.a1'], 'contains': ['48.c1.a1', '48.g1.a1', '48.m1.a1', '168.w1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 672, 192, 4], 'label': '1344.8544.24.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051828
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '12.i1.a1', '12.n1.a1', '12.v1.a1'], 'contains': ['48.g1.a1', '48.i1.a1', '48.k1.a1', '168.x1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [3, 672, 192, 4], 'label': '1344.8544.24.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051829
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.j1.a1', '12.o1.a1', '12.v1.a1', '12.ba1.a1', '12.ba1.b1', '12.bb1.a1', '12.bb1.b1'], 'contains': ['48.b1.a1', '48.g1.a1', '168.y1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [4, 672, 192, 336], 'label': '1344.8544.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051830
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bb1', '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.l1.a1', '12.k1.a1', '12.p1.a1', '12.w1.b1', '12.z1.a1', '12.bb1.a1', '12.bd1.a1', '12.be1.a1'], 'contains': ['48.b1.a1', '48.l1.a1', '168.bb1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [205, 672, 192, 336], 'label': '1344.8544.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051831
    {'ambient': '1344.8544', '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.d1.a1', 'complements': ['336.o1.a1', '336.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.n1.a1', '8.n1.b1', '12.c1.a1', '28.b1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 448, 192, 168, 336], 'label': '1344.8544.4.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.b1.a1', '8.n1.a1', '8.n1.b1', '12.c1.a1', '28.b1.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: 74051832
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bb1', '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.l1.b1', '12.k1.a1', '12.p1.b1', '12.w1.a1', '12.z1.b1', '12.bb1.b1', '12.bd1.b1', '12.be1.b1'], 'contains': ['48.b1.a1', '48.l1.b1', '168.bb1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [204, 672, 192, 336], 'label': '1344.8544.24.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051833
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.j1.a1', '12.q1.a1', '12.u1.a1', '12.bc1.a1', '12.bc1.b1', '12.be1.a1', '12.be1.b1'], 'contains': ['48.b1.a1', '48.m1.a1', '168.bc1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 672, 192, 336], 'label': '1344.8544.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051834
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.l1.a1', '12.r1.a1', '12.x1.b1', '12.z1.b1', '12.ba1.b1', '12.bc1.a1', '12.bd1.a1'], 'contains': ['48.b1.a1', '168.bd1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [58, 1008, 672, 192], 'label': '1344.8544.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051835
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.l1.a1', '12.r1.b1', '12.x1.a1', '12.z1.a1', '12.ba1.a1', '12.bc1.b1', '12.bd1.b1'], 'contains': ['48.b1.a1', '168.bd1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [59, 1008, 672, 192], 'label': '1344.8544.24.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051836
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '12.b1.a1', '12.s1.a1', '12.y1.a1'], 'contains': ['48.c1.a1', '48.j1.a1', '48.j1.b1', '168.be1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 672, 192, 750], 'label': '1344.8544.24.be1.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.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051837
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bf1', '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.bf1.a1', '12.k1.a1', '12.s1.a1', '12.y1.a1'], 'contains': ['48.c1.a1', '48.l1.a1', '48.l1.b1', '168.bf1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 672, 192, 204], 'label': '1344.8544.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051838
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bg1', '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.bg1.a1', '12.m1.a1', '12.p1.a1', '12.y1.a1'], 'contains': ['48.h1.a1', '48.j1.a1', '48.l1.a1', '168.bg1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [205, 672, 192, 562], 'label': '1344.8544.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051839
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bg1', '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.bg1.b1', '12.m1.a1', '12.p1.b1', '12.y1.a1'], 'contains': ['48.h1.a1', '48.j1.b1', '48.l1.b1', '168.bg1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [562, 672, 192, 204], 'label': '1344.8544.24.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051840
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '12.i1.a1', '12.q1.a1', '12.t1.a1'], 'contains': ['48.h1.a1', '48.k1.a1', '48.m1.a1', '168.bh1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [901, 672, 192, 562], 'label': '1344.8544.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051841
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bi1', '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.bi1.a1', '12.m1.a1', '12.s1.a1', '12.w1.a1'], 'contains': ['48.i1.a1', '48.j1.a1', '48.l1.b1', '168.bi1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [899, 672, 192, 204], 'label': '1344.8544.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051860
    {'ambient': '1344.8544', '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': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '14.b1.a1'], 'contains': ['56.e1.a1', '56.n1.a1', '56.p1.a1', '56.u1.a1', '56.v1.a1', '56.x1.a1', '56.y1.a1', '84.l1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 448, 2, 4, 672], 'label': '1344.8544.28.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: 74051842
    {'ambient': '1344.8544', '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': '48.b1.a1', 'complements': ['336.o1.a1', '336.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.o1.a1', '8.o1.b1', '12.l1.a1', '28.c1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 192, 1008, 58, 672], 'label': '1344.8544.4.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '8.o1.b1', '8.o1.a1', '28.c1.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: 74051843
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '24.bi1', '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.bi1.b1', '12.m1.a1', '12.s1.a1', '12.w1.b1'], 'contains': ['48.i1.a1', '48.j1.b1', '48.l1.a1', '168.bi1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [205, 672, 192, 750], 'label': '1344.8544.24.bi1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051844
    {'ambient': '1344.8544', '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': '24.a1.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.e1.a1', '56.f1.a1', '56.g1.a1', '84.c1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 2, 336, 672], 'label': '1344.8544.28.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', '56.e1.a1', '56.d1.a1', '56.g1.a1', '56.f1.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: 74051845
    {'ambient': '1344.8544', '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': '16.d1.a1', 'complements': ['48.o1.a1', '48.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '14.a1.a1', '14.d1.a1', '14.g1.a1'], 'contains': ['56.b1.a1', '56.h1.a1', '56.h1.b1', '84.a1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 168, 448, 336], 'label': '1344.8544.28.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.f1.a1', '14.a1.a1'], 'normal_contains': ['56.b1.a1', '56.h1.a1', '56.h1.b1', '84.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: 74051846
    {'ambient': '1344.8544', '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': '48.b1.a1', 'complements': ['48.o1.a1', '48.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '14.a1.a1', '14.e1.a1', '14.f1.a1'], 'contains': ['56.b1.a1', '56.i1.a1', '56.i1.b1', '84.j1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 58, 1008, 672], 'label': '1344.8544.28.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.c1.a1', 'normal_contained_in': ['4.g1.a1', '14.a1.a1'], 'normal_contains': ['56.b1.a1', '56.i1.b1', '56.i1.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: 74051847
    {'ambient': '1344.8544', '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': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '14.a1.a1', '14.h1.b1', '14.i1.a1'], 'contains': ['56.d1.a1', '56.h1.a1', '56.i1.a1', '84.p1.a1'], 'core': '28.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 448, 168, 336, 672], 'label': '1344.8544.28.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.d1.a1', 'normal_contained_in': ['4.k1.a1', '14.a1.a1'], 'normal_contains': ['56.d1.a1', '56.h1.a1', '56.i1.a1'], 'normalizer': '1.a1.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: 74051848
    {'ambient': '1344.8544', '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': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.b1', '14.a1.a1', '14.h1.a1', '14.i1.b1'], 'contains': ['56.d1.a1', '56.h1.b1', '56.i1.b1', '84.p1.b1'], 'core': '28.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 2, 336, 672], 'label': '1344.8544.28.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.d1.b1', 'normal_contained_in': ['4.k1.b1', '14.a1.a1'], 'normal_contains': ['56.d1.a1', '56.h1.b1', '56.i1.b1'], 'normalizer': '1.a1.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: 74051849
    {'ambient': '1344.8544', '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': '48.b1.a1', 'complements': ['48.o1.a1', '48.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '14.a1.a1', '14.j1.b1', '14.k1.a1'], 'contains': ['56.f1.a1', '56.h1.a1', '56.i1.b1', '84.v1.a1'], 'core': '28.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 448, 168, 336, 672], 'label': '1344.8544.28.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.e1.a1', 'normal_contained_in': ['4.o1.a1', '14.a1.a1'], 'normal_contains': ['56.f1.a1', '56.h1.a1', '56.i1.b1'], 'normalizer': '1.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: 74051850
    {'ambient': '1344.8544', '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': '48.b1.a1', 'complements': ['48.o1.a1', '48.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '14.a1.a1', '14.j1.a1', '14.k1.b1'], 'contains': ['56.f1.a1', '56.h1.b1', '56.i1.a1', '84.v1.b1'], 'core': '28.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 58, 336, 672], 'label': '1344.8544.28.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.e1.b1', 'normal_contained_in': ['4.o1.b1', '14.a1.a1'], 'normal_contains': ['56.f1.a1', '56.h1.b1', '56.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051851
    {'ambient': '1344.8544', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '14.b1.a1'], 'contains': ['56.a1.a1', '56.j1.a1', '56.k1.a1', '56.n1.a1', '56.p1.a1', '56.q1.a1', '56.r1.a1', '84.b1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 448, 2, 4, 672], 'label': '1344.8544.28.f1.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.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: 74051852
    {'ambient': '1344.8544', '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': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '14.c1.a1'], 'contains': ['56.a1.a1', '56.l1.a1', '56.m1.a1', '56.o1.a1', '56.o1.b1', '56.s1.a1', '56.s1.b1', '84.d1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 448, 2, 204, 672], 'label': '1344.8544.28.g1.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.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: 74051853
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.a1', '2.h1.b1'], 'contains': ['8.d1.a1', '8.h1.a1', '8.i1.a1', '8.t1.a1', '8.z1.a1', '12.o1.a1', '28.o1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 336, 672, 4, 448], 'label': '1344.8544.4.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1', '2.h1.a1', '2.h1.b1'], 'normal_contains': ['8.d1.a1', '8.h1.a1', '8.i1.a1'], 'normalizer': '1.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: 74051854
    {'ambient': '1344.8544', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '14.b1.a1'], 'contains': ['56.c1.a1', '56.j1.a1', '56.k1.a1', '56.t1.a1', '56.v1.a1', '56.y1.a1', '56.bh1.a1', '84.e1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 448, 562, 4, 672], 'label': '1344.8544.28.h1.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.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: 74051855
    {'ambient': '1344.8544', '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': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.b1.a1', '14.d1.a1', '14.e1.a1'], 'contains': ['56.b1.a1', '56.j1.a1', '56.u1.a1', '56.w1.a1', '56.bb1.a1', '84.f1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 6, 336, 448], 'label': '1344.8544.28.i1.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.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: 74051856
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.b1.a1', '14.f1.a1', '14.g1.a1'], 'contains': ['56.b1.a1', '56.k1.a1', '56.x1.a1', '56.z1.a1', '56.bd1.a1', '84.g1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 4, 336, 672], 'label': '1344.8544.28.j1.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.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: 74051857
    {'ambient': '1344.8544', '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': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.c1.a1', '14.d1.a1', '14.f1.a1'], 'contains': ['56.b1.a1', '56.l1.a1', '56.ba1.a1', '56.ba1.b1', '56.be1.a1', '84.h1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 750, 336, 448], 'label': '1344.8544.28.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.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: 74051858
    {'ambient': '1344.8544', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.c1.a1', '14.e1.a1', '14.g1.a1'], 'contains': ['56.b1.a1', '56.m1.a1', '56.bc1.a1', '56.bc1.b1', '56.bf1.a1', '84.i1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 448, 204, 336, 672], 'label': '1344.8544.28.l1.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.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: 74051859
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '14.c1.a1'], 'contains': ['56.c1.a1', '56.l1.a1', '56.m1.a1', '56.bg1.a1', '56.bg1.b1', '56.bi1.a1', '56.bi1.b1', '84.k1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 448, 562, 204, 672], 'label': '1344.8544.28.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: 74052060
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '112.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '56.n1.a1'], 'contains': ['224.b1.a1', '224.e1.a1', '224.f1.a1', '336.o1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [2, 4, 448], 'label': '1344.8544.112.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.n1.a1', 'old_label': '112.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051861
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '14.b1.a1', '14.h1.a1', '14.h1.b1'], 'contains': ['56.d1.a1', '56.n1.a1', '56.t1.a1', '56.w1.a1', '56.z1.a1', '84.m1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2, 448, 4, 336, 672], 'label': '1344.8544.28.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.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: 74051862
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '14.c1.a1', '14.h1.a1', '14.i1.a1'], 'contains': ['56.d1.a1', '56.o1.a1', '56.ba1.a1', '56.bc1.a1', '56.bg1.a1', '84.n1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [205, 448, 2, 336, 672], 'label': '1344.8544.28.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.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: 74051863
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '14.c1.a1', '14.h1.b1', '14.i1.b1'], 'contains': ['56.d1.a1', '56.o1.b1', '56.ba1.b1', '56.bc1.b1', '56.bg1.b1', '84.n1.b1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [2, 448, 204, 336, 672], 'label': '1344.8544.28.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051864
    {'ambient': '1344.8544', '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': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.d1.a1', '8.j1.a1', '8.l1.a1', '8.u1.a1', '8.bg1.a1', '12.p1.a1', '28.p1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [205, 192, 336, 672, 2, 448], 'label': '1344.8544.4.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.b1.a1', '2.h1.a1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.j1.a1', '8.l1.a1'], 'normalizer': '1.a1.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: 74051865
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '14.b1.a1', '14.i1.a1', '14.i1.b1'], 'contains': ['56.d1.a1', '56.p1.a1', '56.bb1.a1', '56.bd1.a1', '56.bh1.a1', '84.o1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 2, 336, 672], 'label': '1344.8544.28.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.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: 74051866
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.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.bc1.a1', '14.c1.a1'], 'contains': ['56.e1.a1', '56.o1.a1', '56.o1.b1', '56.be1.a1', '56.bf1.a1', '56.bi1.a1', '56.bi1.b1', '84.q1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 448, 2, 204, 672], 'label': '1344.8544.28.r1.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.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051867
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '14.b1.a1'], 'contains': ['56.g1.a1', '56.q1.a1', '56.r1.a1', '56.t1.a1', '56.u1.a1', '56.x1.a1', '56.bh1.a1', '84.r1.a1'], 'core': '56.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 448, 562, 4, 672], 'label': '1344.8544.28.s1.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.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051868
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '14.b1.a1', '14.j1.a1', '14.j1.b1'], 'contains': ['56.f1.a1', '56.q1.a1', '56.v1.a1', '56.w1.a1', '56.bd1.a1', '84.s1.a1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 6, 336, 672], 'label': '1344.8544.28.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051869
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '14.b1.a1', '14.k1.a1', '14.k1.b1'], 'contains': ['56.f1.a1', '56.r1.a1', '56.y1.a1', '56.z1.a1', '56.bb1.a1', '84.t1.a1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 448, 4, 336, 672], 'label': '1344.8544.28.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051870
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.v1', '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.n1.a1', '14.c1.a1', '14.j1.a1', '14.k1.a1'], 'contains': ['56.f1.a1', '56.s1.a1', '56.ba1.a1', '56.bc1.b1', '56.bi1.a1', '84.u1.a1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [3, 448, 204, 336, 672], 'label': '1344.8544.28.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051871
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.v1', '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.n1.b1', '14.c1.a1', '14.j1.b1', '14.k1.b1'], 'contains': ['56.f1.a1', '56.s1.b1', '56.ba1.b1', '56.bc1.a1', '56.bi1.b1', '84.u1.b1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [973, 448, 750, 336, 672], 'label': '1344.8544.28.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051872
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.w1', '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.be1.a1', '14.c1.a1'], 'contains': ['56.g1.a1', '56.s1.a1', '56.s1.b1', '56.be1.a1', '56.bf1.a1', '56.bg1.a1', '56.bg1.b1', '84.w1.a1'], 'core': '56.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 448, 562, 204, 672], 'label': '1344.8544.28.w1.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.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051873
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.x1', '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.p1.a1', '14.d1.a1', '14.h1.a1', '14.j1.a1'], 'contains': ['56.h1.b1', '56.w1.a1', '56.ba1.a1', '84.x1.a1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 672, 6, 448, 336], 'label': '1344.8544.28.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051874
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.x1', '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.p1.b1', '14.d1.a1', '14.h1.b1', '14.j1.b1'], 'contains': ['56.h1.a1', '56.w1.a1', '56.ba1.b1', '84.x1.b1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [6, 672, 168, 448, 336], 'label': '1344.8544.28.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051875
    {'ambient': '1344.8544', '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': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.b1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.j1.b1', '8.l1.b1', '8.u1.b1', '8.bg1.b1', '12.p1.b1', '28.p1.b1'], 'core': '4.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 336, 672, 204, 448], 'label': '1344.8544.4.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': ['2.b1.a1', '2.h1.b1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.j1.b1', '8.l1.b1'], 'normalizer': '1.a1.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: 74051876
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.y1', '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.q1.a1', '14.e1.a1', '14.h1.a1', '14.j1.b1'], 'contains': ['56.i1.b1', '56.w1.a1', '56.bc1.a1', '84.y1.a1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [397, 448, 6, 1008, 672], 'label': '1344.8544.28.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051877
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.y1', '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.q1.b1', '14.e1.a1', '14.h1.b1', '14.j1.a1'], 'contains': ['56.i1.a1', '56.w1.a1', '56.bc1.b1', '84.y1.b1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [58, 448, 204, 1008, 672], 'label': '1344.8544.28.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051878
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.z1', '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.r1.a1', '14.f1.a1', '14.h1.a1', '14.k1.a1'], 'contains': ['56.i1.b1', '56.z1.a1', '56.ba1.a1', '84.z1.a1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [59, 448, 4, 1008, 672], 'label': '1344.8544.28.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051879
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.z1', '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.r1.b1', '14.f1.a1', '14.h1.b1', '14.k1.b1'], 'contains': ['56.i1.a1', '56.z1.a1', '56.ba1.b1', '84.z1.b1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [58, 448, 4, 1008, 672], 'label': '1344.8544.28.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051880
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.ba1', '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.s1.a1', '14.g1.a1', '14.h1.a1', '14.k1.b1'], 'contains': ['56.h1.b1', '56.z1.a1', '56.bc1.a1', '84.ba1.a1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 4, 336, 672], 'label': '1344.8544.28.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051881
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.ba1', '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.s1.b1', '14.g1.a1', '14.h1.b1', '14.k1.a1'], 'contains': ['56.h1.a1', '56.z1.a1', '56.bc1.b1', '84.ba1.b1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [4, 448, 168, 336, 672], 'label': '1344.8544.28.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051882
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.bb1', '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.t1.a1', '14.d1.a1', '14.i1.a1', '14.k1.a1'], 'contains': ['56.h1.a1', '56.ba1.a1', '56.bb1.a1', '84.bb1.a1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [7, 672, 168, 448, 1008], 'label': '1344.8544.28.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051883
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.bb1', '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.t1.b1', '14.d1.a1', '14.i1.b1', '14.k1.b1'], 'contains': ['56.h1.b1', '56.ba1.b1', '56.bb1.a1', '84.bb1.b1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 672, 750, 448, 336], 'label': '1344.8544.28.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051884
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.bc1', '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.u1.a1', '14.f1.a1', '14.i1.a1', '14.j1.a1'], 'contains': ['56.i1.a1', '56.ba1.a1', '56.bd1.a1', '84.bc1.a1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 58, 1008, 672], 'label': '1344.8544.28.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051885
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.bc1', '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.u1.b1', '14.f1.a1', '14.i1.b1', '14.j1.b1'], 'contains': ['56.i1.b1', '56.ba1.b1', '56.bd1.a1', '84.bc1.b1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [581, 448, 750, 1008, 672], 'label': '1344.8544.28.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051886
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.i1.a1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.k1.a1', '8.m1.a1', '8.v1.a1', '8.bh1.a1', '12.q1.a1', '28.q1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 336, 672, 2, 448], 'label': '1344.8544.4.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.a1.a1', '2.i1.a1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.k1.a1', '8.m1.a1'], 'normalizer': '1.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: 74051887
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.bd1', '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.v1.a1', '14.e1.a1', '14.i1.a1', '14.k1.b1'], 'contains': ['56.i1.a1', '56.bb1.a1', '56.bc1.a1', '84.bd1.a1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [205, 448, 58, 336, 672], 'label': '1344.8544.28.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051888
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.bd1', '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.v1.b1', '14.e1.a1', '14.i1.b1', '14.k1.a1'], 'contains': ['56.i1.b1', '56.bb1.a1', '56.bc1.b1', '84.bd1.b1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [59, 448, 204, 1008, 672], 'label': '1344.8544.28.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051889
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.be1', '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.w1.a1', '14.g1.a1', '14.i1.a1', '14.j1.b1'], 'contains': ['56.h1.a1', '56.bc1.a1', '56.bd1.a1', '84.be1.a1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 448, 168, 1008, 672], 'label': '1344.8544.28.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051890
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '28.be1', '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.w1.b1', '14.g1.a1', '14.i1.b1', '14.j1.a1'], 'contains': ['56.h1.b1', '56.bc1.b1', '56.bd1.a1', '84.be1.b1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 448, 204, 336, 672], 'label': '1344.8544.28.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051891
    {'ambient': '1344.8544', '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.j1.a1', '16.j1.b1', '16.k1.a1', '16.l1.a1', '16.l1.b1', '16.m1.a1'], '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, 448], 'label': '1344.8544.32.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.e1.a1', '16.d1.a1', '16.g1.a1', '16.f1.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: 74051892
    {'ambient': '1344.8544', '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': '12.c1.a1', 'complements': ['42.g1.a1', '42.k1.a1', '42.d1.a1', '42.j1.b1', '42.f1.a1', '42.k1.b1', '42.e1.a1', '42.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.n1.a1', '16.o1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '224.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 448, 192], 'label': '1344.8544.32.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.a1.a1', '224.b1.a1'], 'normalizer': '1.a1.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: 74051893
    {'ambient': '1344.8544', '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': '12.c1.a1', 'complements': ['42.g1.a1', '42.k1.a1', '42.d1.a1', '42.j1.b1', '42.f1.a1', '42.k1.b1', '42.e1.a1', '42.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.n1.b1', '16.o1.b1'], 'contains': ['64.a1.a1', '96.c1.b1', '224.b1.b1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [226, 448, 192], 'label': '1344.8544.32.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.b1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.a1.a1', '224.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051894
    {'ambient': '1344.8544', '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': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.n1.a1', '16.n1.b1'], 'contains': ['64.a1.a1', '96.b1.a1', '224.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 192, 448], 'label': '1344.8544.32.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74051895
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.n1.a1', '16.n1.b1'], 'contains': ['64.a1.a1', '96.d1.a1', '224.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1235, 448, 192], 'label': '1344.8544.32.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74051896
    {'ambient': '1344.8544', '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.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.o1.a1', '16.o1.b1'], 'contains': ['64.a1.a1', '96.e1.a1', '224.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 192, 448], 'label': '1344.8544.32.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.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: 74051897
    {'ambient': '1344.8544', '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': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.b1', '2.i1.a1'], 'contains': ['8.d1.a1', '8.n1.a1', '8.o1.a1', '12.r1.a1', '28.d1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 448, 192, 336, 168, 672], 'label': '1344.8544.4.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.c1.a1', '2.h1.b1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.n1.a1', '8.o1.a1', '28.d1.a1'], 'normalizer': '1.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: 74051898
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.o1.a1', '16.o1.b1'], 'contains': ['64.a1.a1', '96.f1.a1', '224.f1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [4, 192, 448], 'label': '1344.8544.32.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '32.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051899
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.c1.a1', '84.e1.a1', '84.f1.a1', '84.g1.a1', '84.l1.a1', '84.m1.a1', '84.o1.a1', '84.r1.a1', '84.s1.a1', '84.t1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 2, 4, 336], 'label': '1344.8544.42.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: 74051900
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.d1.a1', '84.h1.a1', '84.i1.a1', '84.k1.a1', '84.n1.a1', '84.n1.b1', '84.q1.a1', '84.u1.a1', '84.u1.b1', '84.w1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 898, 204, 336], 'label': '1344.8544.42.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: 74051901
    {'ambient': '1344.8544', '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': '24.m1.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.j1.a1', '84.p1.a1', '84.p1.b1', '84.v1.a1', '84.v1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 2, 168], 'label': '1344.8544.42.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: 74051902
    {'ambient': '1344.8544', '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': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.f1.a1', '84.h1.a1', '84.x1.a1', '84.x1.b1', '84.bb1.a1', '84.bb1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 6, 168], 'label': '1344.8544.42.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: 74051903
    {'ambient': '1344.8544', '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.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.f1.a1', '84.i1.a1', '84.j1.a1', '84.y1.a1', '84.y1.b1', '84.bd1.a1', '84.bd1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 58, 204], 'label': '1344.8544.42.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: 74051904
    {'ambient': '1344.8544', '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.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '14.f1.a1', '21.a1.a1'], 'contains': ['84.g1.a1', '84.h1.a1', '84.j1.a1', '84.z1.a1', '84.z1.b1', '84.bc1.a1', '84.bc1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 506, 4], 'label': '1344.8544.42.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: 74051905
    {'ambient': '1344.8544', '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': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '14.g1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.g1.a1', '84.i1.a1', '84.ba1.a1', '84.ba1.b1', '84.be1.a1', '84.be1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 4, 168], 'label': '1344.8544.42.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: 74051906
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '42.h1', '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': ['6.h1.a1', '14.h1.a1', '21.a1.a1'], 'contains': ['84.m1.a1', '84.n1.a1', '84.p1.b1', '84.x1.a1', '84.y1.a1', '84.z1.a1', '84.ba1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 2, 4], 'label': '1344.8544.42.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051907
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '42.h1', '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': ['6.h1.b1', '14.h1.b1', '21.a1.a1'], 'contains': ['84.m1.a1', '84.n1.b1', '84.p1.a1', '84.x1.b1', '84.y1.b1', '84.z1.b1', '84.ba1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2, 4, 168], 'label': '1344.8544.42.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051908
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': ['672.f1.a1', '672.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '4.n1.a1', '4.n1.b1', '4.y1.a1', '4.ba1.a1', '4.bc1.a1', '4.be1.a1', '6.c1.a1', '14.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 204, 336, 2, 192, 672], 'label': '1344.8544.2.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.d1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '4.n1.a1', '4.n1.b1'], '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: 74051909
    {'ambient': '1344.8544', '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': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.a1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.n1.b1', '8.o1.b1', '12.r1.b1', '28.d1.b1'], 'core': '4.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 192, 336, 2, 672], 'label': '1344.8544.4.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.b1', 'normal_contained_in': ['2.c1.a1', '2.h1.a1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.n1.b1', '8.o1.b1', '28.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051910
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '42.i1', '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': ['6.i1.a1', '14.i1.a1', '21.a1.a1'], 'contains': ['84.n1.a1', '84.o1.a1', '84.p1.a1', '84.bb1.a1', '84.bc1.a1', '84.bd1.a1', '84.be1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 2, 168], 'label': '1344.8544.42.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051911
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '42.i1', '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': ['6.i1.b1', '14.i1.b1', '21.a1.a1'], 'contains': ['84.n1.b1', '84.o1.a1', '84.p1.b1', '84.bb1.b1', '84.bc1.b1', '84.bd1.b1', '84.be1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 898, 204], 'label': '1344.8544.42.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051912
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '42.j1', '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': ['6.j1.a1', '14.j1.a1', '21.a1.a1'], 'contains': ['84.s1.a1', '84.u1.a1', '84.v1.b1', '84.x1.a1', '84.y1.b1', '84.bc1.a1', '84.be1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 58, 204], 'label': '1344.8544.42.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051913
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '42.j1', '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': ['6.j1.b1', '14.j1.b1', '21.a1.a1'], 'contains': ['84.s1.a1', '84.u1.b1', '84.v1.a1', '84.x1.b1', '84.y1.a1', '84.bc1.b1', '84.be1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 6, 168], 'label': '1344.8544.42.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051914
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '42.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': ['6.k1.a1', '14.k1.a1', '21.a1.a1'], 'contains': ['84.t1.a1', '84.u1.a1', '84.v1.a1', '84.z1.a1', '84.ba1.b1', '84.bb1.a1', '84.bd1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [3, 4, 168], 'label': '1344.8544.42.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051915
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '42.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': ['6.k1.b1', '14.k1.b1', '21.a1.a1'], 'contains': ['84.t1.a1', '84.u1.b1', '84.v1.b1', '84.z1.b1', '84.ba1.a1', '84.bb1.b1', '84.bd1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 506, 4], 'label': '1344.8544.42.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051916
    {'ambient': '1344.8544', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [337, 192, 672], 'label': '1344.8544.48.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: 74051917
    {'ambient': '1344.8544', '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': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.e1.a1', '24.e1.b1', '24.m1.a1', '24.s1.a1', '24.ba1.a1', '24.bb1.a1', '24.bb1.b1', '24.bc1.a1', '24.bd1.a1', '24.bd1.b1'], 'contains': ['96.a1.a1', '336.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 672, 192], 'label': '1344.8544.48.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.d1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.c1.b1', '24.d1.a1', '24.e1.a1', '24.e1.b1'], '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: 74051918
    {'ambient': '1344.8544', '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': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.a1.a1', '24.n1.a1', '24.t1.a1', '24.w1.a1', '24.y1.a1', '24.be1.a1', '24.bf1.a1'], 'contains': ['96.a1.a1', '336.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 192], 'label': '1344.8544.48.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.e1.a1', '24.a1.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: 74051919
    {'ambient': '1344.8544', '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': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.f1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1', '24.o1.b1', '24.p1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.c1.b1', '336.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 672], 'label': '1344.8544.48.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051920
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.j1.a1', '2.j1.b1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.m1.a1', '8.w1.a1', '8.bb1.a1', '12.u1.a1', '28.t1.a1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 336, 672, 6, 448], 'label': '1344.8544.4.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.a1.a1', '2.j1.a1', '2.j1.b1'], 'normal_contains': ['8.f1.a1', '8.h1.a1', '8.m1.a1'], 'normalizer': '1.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: 74051921
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.f1.a1', '24.q1.a1', '24.r1.a1', '24.s1.a1', '24.t1.a1', '24.u1.a1', '24.u1.b1'], 'contains': ['96.a1.a1', '96.d1.a1', '336.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1235, 192, 672], 'label': '1344.8544.48.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.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: 74051922
    {'ambient': '1344.8544', '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': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.b1.a1', '24.g1.a1', '24.l1.a1', '24.q1.a1', '24.v1.a1', '24.w1.a1', '24.x1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '336.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 192, 672], 'label': '1344.8544.48.f1.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.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: 74051923
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.h1.a1', '24.l1.a1', '24.r1.a1', '24.v1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '336.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [4, 192, 672], 'label': '1344.8544.48.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.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: 74051924
    {'ambient': '1344.8544', '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': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.i1.a1', '24.m1.a1', '24.t1.a1', '24.v1.a1', '24.bg1.a1', '24.bg1.b1', '24.bh1.a1'], 'contains': ['96.a1.a1', '336.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [562, 672, 192], 'label': '1344.8544.48.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.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: 74051925
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.i1.a1', '24.n1.a1', '24.s1.a1', '24.x1.a1', '24.z1.a1', '24.bi1.a1', '24.bi1.b1'], 'contains': ['96.a1.a1', '336.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 672, 192], 'label': '1344.8544.48.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74051926
    {'ambient': '1344.8544', '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': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.c1.a1', '24.j1.a1', '24.o1.a1', '24.u1.a1', '24.be1.a1', '24.bg1.a1', '24.bi1.a1'], 'contains': ['96.a1.a1', '336.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [751, 192, 672], 'label': '1344.8544.48.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74051927
    {'ambient': '1344.8544', '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': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.c1.b1', '24.j1.a1', '24.o1.b1', '24.u1.b1', '24.be1.a1', '24.bg1.b1', '24.bi1.b1'], 'contains': ['96.a1.a1', '336.j1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [750, 192, 672], 'label': '1344.8544.48.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051928
    {'ambient': '1344.8544', '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': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.d1.a1', '24.g1.a1', '24.p1.a1', '24.r1.a1', '24.w1.a1', '24.z1.a1', '24.bh1.a1'], 'contains': ['96.a1.a1', '336.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [7, 192, 672], 'label': '1344.8544.48.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.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: 74051929
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '48.l1', '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.l1.a1', '24.k1.a1', '24.o1.a1', '24.u1.b1', '24.bb1.a1', '24.bf1.a1', '24.bg1.a1', '24.bi1.b1'], 'contains': ['96.a1.a1', '336.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [205, 192, 672], 'label': '1344.8544.48.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051930
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '48.l1', '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.l1.b1', '24.k1.a1', '24.o1.b1', '24.u1.a1', '24.bb1.b1', '24.bf1.a1', '24.bg1.b1', '24.bi1.a1'], 'contains': ['96.a1.a1', '336.l1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [204, 192, 672], 'label': '1344.8544.48.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051931
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.k1.a1', '2.k1.b1'], 'contains': ['8.f1.a1', '8.i1.a1', '8.k1.a1', '8.x1.a1', '8.bd1.a1', '12.v1.a1', '28.u1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 192, 336, 672, 4, 448], 'label': '1344.8544.4.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.a1.a1', '2.k1.a1', '2.k1.b1'], 'normal_contains': ['8.f1.a1', '8.i1.a1', '8.k1.a1'], 'normalizer': '1.a1.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: 74051932
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.h1.a1', '24.p1.a1', '24.q1.a1', '24.x1.a1', '24.y1.a1', '24.bc1.a1', '24.bh1.a1'], 'contains': ['96.a1.a1', '336.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [5, 192, 672], 'label': '1344.8544.48.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051933
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '48.n1', '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.n1.a1', '24.f1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.d1.a1', '336.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 192, 2], 'label': '1344.8544.48.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051934
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '48.n1', '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.n1.b1', '24.f1.a1'], 'contains': ['96.b1.a1', '96.c1.b1', '96.d1.a1', '336.n1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 192, 226], 'label': '1344.8544.48.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051935
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.l1.a1'], 'contains': ['96.c1.a1', '96.e1.a1', '96.f1.a1', '336.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2, 192, 4], 'label': '1344.8544.48.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051936
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '24.l1.a1'], 'contains': ['96.c1.b1', '96.e1.a1', '96.f1.a1', '336.o1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [674, 192, 4], 'label': '1344.8544.48.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051937
    {'ambient': '1344.8544', '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': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '28.f1.a1', '28.g1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '112.n1.a1', '112.n1.b1', '168.c1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [337, 2, 672, 448], 'label': '1344.8544.56.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.a1.a1', '28.a1.a1'], 'normal_contains': ['112.a1.a1', '112.b1.a1', '112.c1.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: 74051938
    {'ambient': '1344.8544', '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': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1', '28.i1.a1', '28.j1.a1', '28.k1.a1', '28.l1.a1'], 'contains': ['112.a1.a1', '112.d1.a1', '112.e1.a1', '168.a1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 448, 672], 'label': '1344.8544.56.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.b1.a1', 'normal_contained_in': ['8.b1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normal_contains': ['112.a1.a1', '112.e1.a1', '112.d1.a1', '168.a1.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: 74051939
    {'ambient': '1344.8544', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1', '28.h1.a1', '28.m1.a1'], 'contains': ['112.a1.a1', '112.f1.a1', '112.g1.a1', '168.f1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [337, 562, 672, 448], 'label': '1344.8544.56.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.c1.a1', 'normal_contained_in': ['8.c1.a1', '28.a1.a1'], 'normal_contains': ['112.a1.a1', '112.g1.a1', '112.f1.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: 74051940
    {'ambient': '1344.8544', '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': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.a1.a1', '28.d1.a1', '28.d1.b1', '28.o1.a1', '28.p1.a1', '28.p1.b1', '28.q1.a1'], 'contains': ['112.b1.a1', '112.d1.a1', '112.f1.a1', '168.j1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 336, 672, 448], 'label': '1344.8544.56.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.d1.a1', 'normal_contained_in': ['8.d1.a1', '28.a1.a1', '28.d1.a1', '28.d1.b1'], 'normal_contains': ['112.b1.a1', '112.d1.a1', '112.f1.a1'], 'normalizer': '1.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: 74051941
    {'ambient': '1344.8544', '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': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '28.a1.a1', '28.n1.a1', '28.r1.a1'], 'contains': ['112.b1.a1', '112.e1.a1', '112.g1.a1', '168.k1.a1'], 'core': '56.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 2, 672, 448], 'label': '1344.8544.56.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.e1.a1', 'normal_contained_in': ['8.e1.a1', '28.a1.a1'], 'normal_contains': ['112.b1.a1', '112.e1.a1', '112.g1.a1'], 'normalizer': '1.a1.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: 74051942
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.f1.a1', '8.j1.a1', '8.l1.b1', '8.y1.a1', '8.bi1.a1', '12.w1.a1', '28.v1.a1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 192, 336, 672, 204, 448], 'label': '1344.8544.4.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.b1.a1', '2.j1.a1', '2.k1.a1'], 'normal_contains': ['8.f1.a1', '8.j1.a1', '8.l1.b1'], 'normalizer': '1.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: 74051943
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '28.a1.a1', '28.e1.a1', '28.e1.b1', '28.t1.a1', '28.u1.a1', '28.v1.a1', '28.v1.b1'], 'contains': ['112.c1.a1', '112.d1.a1', '112.g1.a1', '168.p1.a1'], 'core': '56.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 336, 672, 448], 'label': '1344.8544.56.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.f1.a1', 'normal_contained_in': ['8.f1.a1', '28.a1.a1', '28.e1.a1', '28.e1.b1'], 'normal_contains': ['112.c1.a1', '112.d1.a1', '112.g1.a1'], 'normalizer': '1.a1.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: 74051944
    {'ambient': '1344.8544', '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': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '28.a1.a1', '28.s1.a1', '28.w1.a1'], 'contains': ['112.c1.a1', '112.e1.a1', '112.f1.a1', '168.q1.a1'], 'core': '56.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 562, 672, 448], 'label': '1344.8544.56.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.g1.a1', 'normal_contained_in': ['8.g1.a1', '28.a1.a1'], 'normal_contains': ['112.c1.a1', '112.e1.a1', '112.f1.a1'], 'normalizer': '1.a1.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: 74051945
    {'ambient': '1344.8544', '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': '8.n1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '28.b1.a1', '28.d1.a1', '28.e1.a1', '28.x1.b1', '28.ba1.b1', '28.bb1.a1', '28.be1.a1'], 'contains': ['112.d1.a1', '168.b1.a1'], 'core': '56.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168, 448, 336, 672], 'label': '1344.8544.56.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.h1.a1', 'normal_contained_in': ['8.n1.a1', '28.b1.a1', '28.d1.a1', '28.e1.a1'], 'normal_contains': ['112.d1.a1', '168.b1.a1'], 'normalizer': '1.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: 74051946
    {'ambient': '1344.8544', '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': '8.n1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '28.b1.a1', '28.d1.b1', '28.e1.b1', '28.x1.a1', '28.ba1.a1', '28.bb1.b1', '28.be1.b1'], 'contains': ['112.d1.a1', '168.b1.b1'], 'core': '56.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 336, 672], 'label': '1344.8544.56.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.h1.b1', 'normal_contained_in': ['8.n1.b1', '28.b1.a1', '28.d1.b1', '28.e1.b1'], 'normal_contains': ['112.d1.a1', '168.b1.b1'], 'normalizer': '1.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: 74051947
    {'ambient': '1344.8544', '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': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '28.c1.a1', '28.d1.a1', '28.e1.b1', '28.y1.b1', '28.z1.b1', '28.bc1.a1', '28.bd1.a1'], 'contains': ['112.d1.a1', '168.bd1.a1'], 'core': '56.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [58, 1008, 672, 448], 'label': '1344.8544.56.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.i1.a1', 'normal_contained_in': ['8.o1.a1', '28.c1.a1', '28.d1.a1', '28.e1.b1'], 'normal_contains': ['112.d1.a1'], 'normalizer': '1.a1.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: 74051948
    {'ambient': '1344.8544', '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': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '28.c1.a1', '28.d1.b1', '28.e1.a1', '28.y1.a1', '28.z1.a1', '28.bc1.b1', '28.bd1.b1'], 'contains': ['112.d1.a1', '168.bd1.b1'], 'core': '56.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [59, 1008, 672, 448], 'label': '1344.8544.56.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.i1.b1', 'normal_contained_in': ['8.o1.b1', '28.c1.a1', '28.d1.b1', '28.e1.a1'], 'normal_contains': ['112.d1.a1'], 'normalizer': '1.a1.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: 74051949
    {'ambient': '1344.8544', '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': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '28.f1.a1', '28.h1.a1', '28.i1.a1'], 'contains': ['112.a1.a1', '112.h1.a1', '112.k1.a1', '168.d1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 6, 448, 672], 'label': '1344.8544.56.j1.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.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: 74051950
    {'ambient': '1344.8544', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '28.f1.a1', '28.h1.a1', '28.j1.a1'], 'contains': ['112.a1.a1', '112.i1.a1', '112.m1.a1', '168.e1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 4, 672, 448], 'label': '1344.8544.56.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.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: 74051951
    {'ambient': '1344.8544', '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.r1.a1', '28.g1.a1', '28.k1.a1', '28.m1.a1'], 'contains': ['112.a1.a1', '112.j1.a1', '112.j1.b1', '168.g1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 750, 448, 672], 'label': '1344.8544.56.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.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: 74051952
    {'ambient': '1344.8544', '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': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '28.g1.a1', '28.l1.a1', '28.m1.a1'], 'contains': ['112.a1.a1', '112.l1.a1', '112.l1.b1', '168.h1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 204, 672, 448], 'label': '1344.8544.56.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.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: 74051953
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.j1.b1', '2.k1.b1'], 'contains': ['8.f1.a1', '8.j1.b1', '8.l1.a1', '8.y1.b1', '8.bi1.b1', '12.w1.b1', '28.v1.b1'], 'core': '4.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [205, 192, 336, 672, 750, 448], 'label': '1344.8544.4.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': ['2.b1.a1', '2.j1.b1', '2.k1.b1'], 'normal_contains': ['8.f1.a1', '8.j1.b1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051954
    {'ambient': '1344.8544', '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': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '28.f1.a1', '28.n1.a1', '28.o1.a1'], 'contains': ['112.b1.a1', '112.h1.a1', '112.i1.a1', '112.o1.a1', '112.o1.b1', '168.i1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [2, 4, 672, 448], 'label': '1344.8544.56.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.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: 74051955
    {'ambient': '1344.8544', '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': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '28.g1.a1', '28.p1.a1', '28.r1.a1'], 'contains': ['112.b1.a1', '112.j1.a1', '112.l1.a1', '168.l1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [205, 2, 672, 448], 'label': '1344.8544.56.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.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: 74051956
    {'ambient': '1344.8544', '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': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.b1', '28.g1.a1', '28.p1.b1', '28.r1.a1'], 'contains': ['112.b1.a1', '112.j1.b1', '112.l1.b1', '168.l1.b1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [2, 204, 672, 448], 'label': '1344.8544.56.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051957
    {'ambient': '1344.8544', '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': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '28.f1.a1', '28.n1.a1', '28.q1.a1'], 'contains': ['112.b1.a1', '112.k1.a1', '112.m1.a1', '168.m1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5, 2, 672, 448], 'label': '1344.8544.56.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.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: 74051958
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '28.f1.a1', '28.s1.a1', '28.t1.a1'], 'contains': ['112.c1.a1', '112.h1.a1', '112.m1.a1', '168.n1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1237, 6, 672, 448], 'label': '1344.8544.56.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.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: 74052061
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '112.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '56.n1.a1'], 'contains': ['224.b1.b1', '224.e1.a1', '224.f1.a1', '336.o1.b1'], 'core': '224.b1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [226, 4, 448], 'label': '1344.8544.112.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.n1.a1', 'old_label': '112.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051959
    {'ambient': '1344.8544', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '28.f1.a1', '28.s1.a1', '28.u1.a1'], 'contains': ['112.c1.a1', '112.i1.a1', '112.k1.a1', '168.o1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1235, 4, 672, 448], 'label': '1344.8544.56.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.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: 74051960
    {'ambient': '1344.8544', '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': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '28.g1.a1', '28.v1.a1', '28.w1.a1'], 'contains': ['112.c1.a1', '112.j1.a1', '112.l1.b1', '168.r1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1235, 204, 672, 448], 'label': '1344.8544.56.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.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: 74051961
    {'ambient': '1344.8544', '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': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.b1', '28.g1.a1', '28.v1.b1', '28.w1.a1'], 'contains': ['112.c1.a1', '112.j1.b1', '112.l1.a1', '168.r1.b1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [861, 750, 672, 448], 'label': '1344.8544.56.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051962
    {'ambient': '1344.8544', '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.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '28.h1.a1', '28.o1.a1', '28.s1.a1'], 'contains': ['112.f1.a1', '112.h1.a1', '112.i1.a1', '168.s1.a1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [562, 4, 672, 448], 'label': '1344.8544.56.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.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: 74051963
    {'ambient': '1344.8544', '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': '56.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '28.i1.a1', '28.n1.a1', '28.s1.a1'], 'contains': ['112.e1.a1', '112.h1.a1', '112.k1.a1', '168.t1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 6, 448, 672], 'label': '1344.8544.56.u1.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.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: 74051964
    {'ambient': '1344.8544', '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': '48.b1.a1', 'complements': ['336.o1.a1', '336.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.j1.b1', '2.k1.a1'], 'contains': ['8.f1.a1', '8.n1.a1', '8.o1.b1', '12.x1.a1', '28.e1.a1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 448, 192, 336, 168, 672], 'label': '1344.8544.4.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.c1.a1', '2.j1.b1', '2.k1.a1'], 'normal_contains': ['8.f1.a1', '8.n1.a1', '8.o1.b1', '28.e1.a1'], 'normalizer': '1.a1.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: 74051965
    {'ambient': '1344.8544', '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': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '28.h1.a1', '28.n1.a1', '28.t1.a1'], 'contains': ['112.g1.a1', '112.h1.a1', '112.m1.a1', '168.u1.a1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5, 6, 672, 448], 'label': '1344.8544.56.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.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: 74051966
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '28.i1.a1', '28.o1.a1', '28.t1.a1', '28.x1.a1', '28.x1.b1', '28.y1.a1', '28.y1.b1'], 'contains': ['112.d1.a1', '112.h1.a1', '168.v1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [6, 336, 448, 672], 'label': '1344.8544.56.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051967
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '28.j1.a1', '28.n1.a1', '28.s1.a1'], 'contains': ['112.e1.a1', '112.i1.a1', '112.m1.a1', '168.w1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 4, 672, 448], 'label': '1344.8544.56.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051968
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '28.h1.a1', '28.n1.a1', '28.u1.a1'], 'contains': ['112.g1.a1', '112.i1.a1', '112.k1.a1', '168.x1.a1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 4, 672, 448], 'label': '1344.8544.56.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051969
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '28.j1.a1', '28.o1.a1', '28.u1.a1', '28.z1.a1', '28.z1.b1', '28.ba1.a1', '28.ba1.b1'], 'contains': ['112.d1.a1', '112.i1.a1', '168.y1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [4, 336, 672, 448], 'label': '1344.8544.56.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051970
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.ba1', '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.j1.a1', '28.k1.a1', '28.p1.a1', '28.v1.a1', '28.x1.a1', '28.z1.a1', '28.bb1.a1', '28.bc1.a1'], 'contains': ['112.d1.a1', '112.j1.a1', '168.z1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [751, 336, 448, 672], 'label': '1344.8544.56.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051971
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.ba1', '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.j1.b1', '28.k1.a1', '28.p1.b1', '28.v1.b1', '28.x1.b1', '28.z1.b1', '28.bb1.b1', '28.bc1.b1'], 'contains': ['112.d1.a1', '112.j1.b1', '168.z1.b1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [750, 336, 448, 672], 'label': '1344.8544.56.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051972
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '28.i1.a1', '28.q1.a1', '28.u1.a1', '28.bb1.a1', '28.bb1.b1', '28.bd1.a1', '28.bd1.b1'], 'contains': ['112.d1.a1', '112.k1.a1', '168.ba1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [7, 336, 448, 672], 'label': '1344.8544.56.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051973
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bc1', '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.l1.a1', '28.l1.a1', '28.p1.a1', '28.v1.b1', '28.y1.a1', '28.ba1.a1', '28.bd1.a1', '28.be1.a1'], 'contains': ['112.d1.a1', '112.l1.a1', '168.bb1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [205, 336, 672, 448], 'label': '1344.8544.56.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051974
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bc1', '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.l1.b1', '28.l1.a1', '28.p1.b1', '28.v1.a1', '28.y1.b1', '28.ba1.b1', '28.bd1.b1', '28.be1.b1'], 'contains': ['112.d1.a1', '112.l1.b1', '168.bb1.b1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [204, 336, 672, 448], 'label': '1344.8544.56.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051975
    {'ambient': '1344.8544', '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': '48.b1.a1', 'complements': ['336.o1.a1', '336.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.j1.a1', '2.k1.b1'], 'contains': ['8.f1.a1', '8.n1.b1', '8.o1.a1', '12.x1.b1', '28.e1.b1'], 'core': '4.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 192, 336, 58, 672], 'label': '1344.8544.4.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': ['2.c1.a1', '2.j1.a1', '2.k1.b1'], 'normal_contains': ['8.f1.a1', '8.n1.b1', '8.o1.a1', '28.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051976
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '28.j1.a1', '28.q1.a1', '28.t1.a1', '28.bc1.a1', '28.bc1.b1', '28.be1.a1', '28.be1.b1'], 'contains': ['112.d1.a1', '112.m1.a1', '168.bc1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [5, 336, 672, 448], 'label': '1344.8544.56.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051977
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.be1', '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.be1.a1', '28.k1.a1', '28.r1.a1', '28.w1.a1'], 'contains': ['112.e1.a1', '112.j1.a1', '112.j1.b1', '168.be1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 750, 448, 672], 'label': '1344.8544.56.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051978
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bf1', '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.bf1.a1', '28.l1.a1', '28.r1.a1', '28.w1.a1'], 'contains': ['112.e1.a1', '112.l1.a1', '112.l1.b1', '168.bf1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 204, 672, 448], 'label': '1344.8544.56.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051979
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bg1', '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.bg1.a1', '28.m1.a1', '28.p1.a1', '28.w1.a1'], 'contains': ['112.f1.a1', '112.j1.a1', '112.l1.a1', '168.bg1.a1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [205, 562, 672, 448], 'label': '1344.8544.56.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051980
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bg1', '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.bg1.b1', '28.m1.a1', '28.p1.b1', '28.w1.a1'], 'contains': ['112.f1.a1', '112.j1.b1', '112.l1.b1', '168.bg1.b1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [562, 204, 672, 448], 'label': '1344.8544.56.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051981
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '28.h1.a1', '28.q1.a1', '28.s1.a1'], 'contains': ['112.f1.a1', '112.k1.a1', '112.m1.a1', '168.bh1.a1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5, 562, 672, 448], 'label': '1344.8544.56.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051982
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bi1', '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.bi1.a1', '28.m1.a1', '28.r1.a1', '28.v1.a1'], 'contains': ['112.g1.a1', '112.j1.a1', '112.l1.b1', '168.bi1.a1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [3, 204, 672, 448], 'label': '1344.8544.56.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051983
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '56.bi1', '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.bi1.b1', '28.m1.a1', '28.r1.a1', '28.v1.b1'], 'contains': ['112.g1.a1', '112.j1.b1', '112.l1.a1', '168.bi1.b1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [973, 750, 672, 448], 'label': '1344.8544.56.bi1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '56.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051984
    {'ambient': '1344.8544', '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.b1.b1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1'], 'contains': ['192.a1.a1', '448.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [448, 192], 'label': '1344.8544.64.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.b1', '32.b1.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: 74051985
    {'ambient': '1344.8544', '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': '8.d1.a1', 'complements': ['16.o1.a1', '16.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.b1.a1', '42.c1.a1', '42.d1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.b1.b1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 168], 'label': '1344.8544.84.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.c1.a1', '28.b1.a1'], 'normal_contains': ['168.a1.a1', '168.b1.a1', '168.b1.b1'], '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: 74051986
    {'ambient': '1344.8544', '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': '224.a1.a1', 'complements': ['336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.h1.a1', '8.j1.a1', '8.n1.b1', '12.d1.a1', '28.x1.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 448, 336, 6, 672], 'label': '1344.8544.4.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.d1.a1', '2.h1.a1', '2.j1.a1'], 'normal_contains': ['8.h1.a1', '8.j1.a1', '8.n1.b1', '12.d1.a1'], 'normalizer': '1.a1.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: 74051987
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '28.f1.a1', '42.a1.a1'], 'contains': ['168.c1.a1', '168.d1.a1', '168.e1.a1', '168.i1.a1', '168.m1.a1', '168.n1.a1', '168.o1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [337, 2, 4], 'label': '1344.8544.84.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: 74051988
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '28.a1.a1', '42.a1.a1', '42.b1.a1', '42.c1.a1'], 'contains': ['168.a1.a1', '168.c1.a1', '168.f1.a1', '168.j1.a1', '168.k1.a1', '168.p1.a1', '168.q1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 2, 336], 'label': '1344.8544.84.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: 74051989
    {'ambient': '1344.8544', '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': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '28.g1.a1', '42.b1.a1'], 'contains': ['168.c1.a1', '168.g1.a1', '168.h1.a1', '168.l1.a1', '168.l1.b1', '168.r1.a1', '168.r1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [337, 898, 204], 'label': '1344.8544.84.d1.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.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: 74051990
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '28.h1.a1', '42.a1.a1'], 'contains': ['168.d1.a1', '168.e1.a1', '168.f1.a1', '168.s1.a1', '168.u1.a1', '168.x1.a1', '168.bh1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [337, 1010, 4], 'label': '1344.8544.84.e1.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.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: 74051991
    {'ambient': '1344.8544', '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': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.i1.a1', '42.a1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.d1.a1', '168.t1.a1', '168.v1.a1', '168.ba1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 6, 336], 'label': '1344.8544.84.f1.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.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: 74051992
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '28.j1.a1', '42.a1.a1', '42.f1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.e1.a1', '168.w1.a1', '168.y1.a1', '168.bc1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 4, 336], 'label': '1344.8544.84.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.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: 74051993
    {'ambient': '1344.8544', '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': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.k1.a1', '42.b1.a1', '42.d1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.g1.a1', '168.z1.a1', '168.z1.b1', '168.be1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 750, 336], 'label': '1344.8544.84.h1.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.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: 74051994
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '28.l1.a1', '42.b1.a1', '42.e1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.h1.a1', '168.bb1.a1', '168.bb1.b1', '168.bf1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [1, 204, 336], 'label': '1344.8544.84.i1.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.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: 74051995
    {'ambient': '1344.8544', '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': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '28.c1.a1', '42.c1.a1', '42.e1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.bd1.a1', '168.bd1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 58], 'label': '1344.8544.84.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.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: 74051996
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '28.m1.a1', '42.b1.a1'], 'contains': ['168.f1.a1', '168.g1.a1', '168.h1.a1', '168.bg1.a1', '168.bg1.b1', '168.bi1.a1', '168.bi1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [337, 562, 204], 'label': '1344.8544.84.k1.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.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: 74051997
    {'ambient': '1344.8544', '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': '224.a1.a1', 'complements': ['336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.b1', '2.j1.b1'], 'contains': ['8.h1.a1', '8.j1.b1', '8.n1.a1', '12.d1.b1', '28.x1.b1'], 'core': '4.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 192, 448, 336, 168, 672], 'label': '1344.8544.4.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': ['2.d1.a1', '2.h1.b1', '2.j1.b1'], 'normal_contains': ['8.h1.a1', '8.j1.b1', '8.n1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74051998
    {'ambient': '1344.8544', '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': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '28.n1.a1', '42.a1.a1'], 'contains': ['168.i1.a1', '168.k1.a1', '168.m1.a1', '168.t1.a1', '168.u1.a1', '168.w1.a1', '168.x1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 2, 4], 'label': '1344.8544.84.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: 74051999
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '28.o1.a1', '42.a1.a1', '42.h1.a1', '42.h1.b1'], 'contains': ['168.i1.a1', '168.j1.a1', '168.s1.a1', '168.v1.a1', '168.y1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [2, 4, 336], 'label': '1344.8544.84.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.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: 74052000
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '28.p1.a1', '42.b1.a1', '42.h1.a1', '42.i1.a1'], 'contains': ['168.j1.a1', '168.l1.a1', '168.z1.a1', '168.bb1.a1', '168.bg1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [653, 2, 336], 'label': '1344.8544.84.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.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: 74052001
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.b1', '28.p1.b1', '42.b1.a1', '42.h1.b1', '42.i1.b1'], 'contains': ['168.j1.a1', '168.l1.b1', '168.z1.b1', '168.bb1.b1', '168.bg1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [898, 204, 336], 'label': '1344.8544.84.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052002
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '28.q1.a1', '42.a1.a1', '42.i1.a1', '42.i1.b1'], 'contains': ['168.j1.a1', '168.m1.a1', '168.ba1.a1', '168.bc1.a1', '168.bh1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 2, 336], 'label': '1344.8544.84.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.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: 74052003
    {'ambient': '1344.8544', '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': '12.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '28.d1.a1', '42.c1.a1', '42.h1.b1', '42.i1.a1'], 'contains': ['168.b1.a1', '168.j1.a1', '168.bd1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 168], 'label': '1344.8544.84.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74052004
    {'ambient': '1344.8544', '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': '12.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.b1', '28.d1.b1', '42.c1.a1', '42.h1.a1', '42.i1.b1'], 'contains': ['168.b1.b1', '168.j1.a1', '168.bd1.b1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 2], 'label': '1344.8544.84.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052005
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '28.r1.a1', '42.b1.a1'], 'contains': ['168.k1.a1', '168.l1.a1', '168.l1.b1', '168.be1.a1', '168.bf1.a1', '168.bi1.a1', '168.bi1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 898, 204], 'label': '1344.8544.84.q1.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.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: 74052006
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '28.s1.a1', '42.a1.a1'], 'contains': ['168.n1.a1', '168.o1.a1', '168.q1.a1', '168.s1.a1', '168.t1.a1', '168.w1.a1', '168.bh1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 1010, 4], 'label': '1344.8544.84.r1.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.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052007
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '28.t1.a1', '42.a1.a1', '42.j1.a1', '42.j1.b1'], 'contains': ['168.n1.a1', '168.p1.a1', '168.u1.a1', '168.v1.a1', '168.bc1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 6, 336], 'label': '1344.8544.84.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052008
    {'ambient': '1344.8544', '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': '672.a1.a1', 'complements': ['336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.j1.b1'], 'contains': ['8.h1.a1', '8.l1.a1', '8.o1.b1', '12.z1.a1', '28.y1.a1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [205, 192, 336, 672, 6, 448], 'label': '1344.8544.4.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.j1.b1'], 'normal_contains': ['8.h1.a1', '8.l1.a1', '8.o1.b1'], 'normalizer': '1.a1.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: 74052009
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '28.u1.a1', '42.a1.a1', '42.k1.a1', '42.k1.b1'], 'contains': ['168.o1.a1', '168.p1.a1', '168.x1.a1', '168.y1.a1', '168.ba1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [3, 4, 336], 'label': '1344.8544.84.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052010
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.u1', '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': ['12.w1.a1', '28.v1.a1', '42.b1.a1', '42.j1.a1', '42.k1.a1'], 'contains': ['168.p1.a1', '168.r1.a1', '168.z1.a1', '168.bb1.b1', '168.bi1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [899, 204, 336], 'label': '1344.8544.84.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052011
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.u1', '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': ['12.w1.b1', '28.v1.b1', '42.b1.a1', '42.j1.b1', '42.k1.b1'], 'contains': ['168.p1.a1', '168.r1.b1', '168.z1.b1', '168.bb1.a1', '168.bi1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [973, 750, 336], 'label': '1344.8544.84.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052012
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '28.e1.a1', '42.c1.a1', '42.j1.b1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.p1.a1', '168.bd1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 168], 'label': '1344.8544.84.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052013
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.b1', '28.e1.b1', '42.c1.a1', '42.j1.a1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.p1.a1', '168.bd1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 58], 'label': '1344.8544.84.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '28.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052014
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.w1', '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': ['12.y1.a1', '28.w1.a1', '42.b1.a1'], 'contains': ['168.q1.a1', '168.r1.a1', '168.r1.b1', '168.be1.a1', '168.bf1.a1', '168.bg1.a1', '168.bg1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 562, 204], 'label': '1344.8544.84.w1.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.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052015
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.x1', '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.d1.a1', '28.x1.a1', '42.d1.a1', '42.h1.a1', '42.j1.a1'], 'contains': ['168.b1.b1', '168.v1.a1', '168.z1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 6], 'label': '1344.8544.84.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052016
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.x1', '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.d1.b1', '28.x1.b1', '42.d1.a1', '42.h1.b1', '42.j1.b1'], 'contains': ['168.b1.a1', '168.v1.a1', '168.z1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [6, 168], 'label': '1344.8544.84.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052017
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.y1', '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.z1.a1', '28.y1.a1', '42.e1.a1', '42.h1.a1', '42.j1.b1'], 'contains': ['168.v1.a1', '168.bb1.a1', '168.bd1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [397, 6], 'label': '1344.8544.84.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052018
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.y1', '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.z1.b1', '28.y1.b1', '42.e1.a1', '42.h1.b1', '42.j1.a1'], 'contains': ['168.v1.a1', '168.bb1.b1', '168.bd1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [58, 204], 'label': '1344.8544.84.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052019
    {'ambient': '1344.8544', '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.b1.a1', 'complements': ['672.f1.a1', '672.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '4.k1.a1', '4.k1.b1', '4.o1.a1', '4.o1.b1', '6.d1.a1', '14.a1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 168, 192, 2, 448, 336], 'label': '1344.8544.2.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.f1.a1', '4.g1.a1', '4.k1.a1', '4.k1.b1', '4.o1.a1', '4.o1.b1', '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: 74052020
    {'ambient': '1344.8544', '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': '672.a1.a1', 'complements': ['336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.b1', '2.j1.a1'], 'contains': ['8.h1.a1', '8.l1.b1', '8.o1.a1', '12.z1.b1', '28.y1.b1'], 'core': '4.q1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [58, 192, 1008, 672, 204, 448], 'label': '1344.8544.4.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': ['2.e1.a1', '2.h1.b1', '2.j1.a1'], 'normal_contains': ['8.h1.a1', '8.l1.b1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052021
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.z1', '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.ba1.a1', '28.z1.a1', '42.f1.a1', '42.h1.a1', '42.k1.a1'], 'contains': ['168.y1.a1', '168.z1.a1', '168.bd1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [507, 4], 'label': '1344.8544.84.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052022
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.z1', '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.ba1.b1', '28.z1.b1', '42.f1.a1', '42.h1.b1', '42.k1.b1'], 'contains': ['168.y1.a1', '168.z1.b1', '168.bd1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [506, 4], 'label': '1344.8544.84.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052023
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.ba1', '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.bb1.a1', '28.ba1.a1', '42.g1.a1', '42.h1.a1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.y1.a1', '168.bb1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 4], 'label': '1344.8544.84.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052024
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.ba1', '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.bb1.b1', '28.ba1.b1', '42.g1.a1', '42.h1.b1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.y1.a1', '168.bb1.b1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [4, 168], 'label': '1344.8544.84.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052025
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.bb1', '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.e1.a1', '28.bb1.a1', '42.d1.a1', '42.i1.a1', '42.k1.a1'], 'contains': ['168.b1.a1', '168.z1.a1', '168.ba1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [7, 168], 'label': '1344.8544.84.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052026
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.bb1', '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.e1.b1', '28.bb1.b1', '42.d1.a1', '42.i1.b1', '42.k1.b1'], 'contains': ['168.b1.b1', '168.z1.b1', '168.ba1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [169, 750], 'label': '1344.8544.84.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052027
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.bc1', '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.bc1.a1', '28.bc1.a1', '42.f1.a1', '42.i1.a1', '42.j1.a1'], 'contains': ['168.z1.a1', '168.bc1.a1', '168.bd1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [901, 58], 'label': '1344.8544.84.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052028
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.bc1', '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.bc1.b1', '28.bc1.b1', '42.f1.a1', '42.i1.b1', '42.j1.b1'], 'contains': ['168.z1.b1', '168.bc1.a1', '168.bd1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [581, 750], 'label': '1344.8544.84.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052029
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.bd1', '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.bd1.a1', '28.bd1.a1', '42.e1.a1', '42.i1.a1', '42.k1.b1'], 'contains': ['168.ba1.a1', '168.bb1.a1', '168.bd1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [205, 58], 'label': '1344.8544.84.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052030
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.bd1', '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.bd1.b1', '28.bd1.b1', '42.e1.a1', '42.i1.b1', '42.k1.a1'], 'contains': ['168.ba1.a1', '168.bb1.b1', '168.bd1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [59, 204], 'label': '1344.8544.84.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052031
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.i1.a1', '8.j1.a1', '8.o1.b1', '12.ba1.a1', '28.z1.a1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [59, 192, 1008, 672, 4, 448], 'label': '1344.8544.4.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.k1.a1'], 'normal_contains': ['8.i1.a1', '8.j1.a1', '8.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052032
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.be1', '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.be1.a1', '28.be1.a1', '42.g1.a1', '42.i1.a1', '42.j1.b1'], 'contains': ['168.b1.a1', '168.bb1.a1', '168.bc1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 168], 'label': '1344.8544.84.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052033
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '84.be1', '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.be1.b1', '28.be1.b1', '42.g1.a1', '42.i1.b1', '42.j1.a1'], 'contains': ['168.b1.b1', '168.bb1.b1', '168.bc1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [169, 204], 'label': '1344.8544.84.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052034
    {'ambient': '1344.8544', '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.j1.a1', '48.j1.b1', '48.k1.a1', '48.l1.a1', '48.l1.b1', '48.m1.a1'], 'contains': ['192.a1.a1', '672.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672, 192], 'label': '1344.8544.96.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: 74052035
    {'ambient': '1344.8544', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.a1.a1', '48.n1.a1', '48.n1.b1'], 'contains': ['192.a1.a1', '672.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 192], 'label': '1344.8544.96.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74052036
    {'ambient': '1344.8544', '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': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.d1.a1', '48.n1.a1', '48.o1.a1'], 'contains': ['192.a1.a1', '672.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192], 'label': '1344.8544.96.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74052037
    {'ambient': '1344.8544', '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': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '48.d1.a1', '48.n1.b1', '48.o1.b1'], 'contains': ['192.a1.a1', '672.c1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [226, 192], 'label': '1344.8544.96.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052038
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.e1.a1', '48.n1.a1', '48.n1.b1'], 'contains': ['192.a1.a1', '672.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1235, 192], 'label': '1344.8544.96.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.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: 74052039
    {'ambient': '1344.8544', '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': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.f1.a1', '48.o1.a1', '48.o1.b1'], 'contains': ['192.a1.a1', '672.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 192], 'label': '1344.8544.96.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.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: 74052040
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.g1.a1', '48.o1.a1', '48.o1.b1'], 'contains': ['192.a1.a1', '672.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [4, 192], 'label': '1344.8544.96.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '96.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052041
    {'ambient': '1344.8544', '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.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1', '56.j1.a1', '56.k1.a1', '56.l1.a1', '56.m1.a1'], 'contains': ['224.a1.a1', '224.c1.a1', '336.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [337, 672, 448], 'label': '1344.8544.112.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1', '56.b1.a1', '56.c1.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: 74052042
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.b1', '2.k1.b1'], 'contains': ['8.i1.a1', '8.j1.b1', '8.o1.a1', '12.ba1.b1', '28.z1.b1'], 'core': '4.r1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [58, 192, 1008, 672, 4, 448], 'label': '1344.8544.4.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.b1', 'normal_contained_in': ['2.f1.a1', '2.h1.b1', '2.k1.b1'], 'normal_contains': ['8.i1.a1', '8.j1.b1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052043
    {'ambient': '1344.8544', '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': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.a1.a1', '56.d1.a1', '56.e1.a1', '56.n1.a1', '56.o1.a1', '56.o1.b1', '56.p1.a1'], 'contains': ['224.a1.a1', '224.b1.a1', '224.b1.b1', '336.d1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 672, 448], 'label': '1344.8544.112.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.b1.a1', 'normal_contained_in': ['16.b1.a1', '56.a1.a1', '56.e1.a1', '56.d1.a1'], 'normal_contains': ['224.a1.a1', '224.b1.b1', '224.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: 74052044
    {'ambient': '1344.8544', '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': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '56.a1.a1', '56.f1.a1', '56.g1.a1', '56.q1.a1', '56.r1.a1', '56.s1.a1', '56.s1.b1'], 'contains': ['224.a1.a1', '224.d1.a1', '336.e1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1235, 672, 448], 'label': '1344.8544.112.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': ['16.c1.a1', '56.a1.a1', '56.g1.a1', '56.f1.a1'], 'normal_contains': ['224.a1.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: 74052045
    {'ambient': '1344.8544', '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': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '56.b1.a1', '56.d1.a1', '56.f1.a1', '56.h1.a1', '56.h1.b1', '56.i1.a1', '56.i1.b1', '56.w1.a1', '56.z1.a1', '56.ba1.a1', '56.ba1.b1', '56.bb1.a1', '56.bc1.a1', '56.bc1.b1', '56.bd1.a1'], 'contains': ['224.a1.a1', '336.b1.a1'], 'core': '112.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336, 448, 672], 'label': '1344.8544.112.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.d1.a1', 'normal_contained_in': ['16.d1.a1', '56.b1.a1', '56.d1.a1', '56.f1.a1', '56.h1.a1', '56.h1.b1', '56.i1.b1', '56.i1.a1'], 'normal_contains': ['224.a1.a1', '336.b1.a1'], 'normalizer': '1.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: 74052046
    {'ambient': '1344.8544', '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': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '56.b1.a1', '56.e1.a1', '56.g1.a1', '56.u1.a1', '56.x1.a1', '56.be1.a1', '56.bf1.a1'], 'contains': ['224.a1.a1', '336.c1.a1'], 'core': '112.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 672], 'label': '1344.8544.112.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.e1.a1', 'normal_contained_in': ['16.e1.a1', '56.b1.a1', '56.e1.a1', '56.g1.a1'], 'normal_contains': ['224.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.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: 74052047
    {'ambient': '1344.8544', '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': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '56.c1.a1', '56.d1.a1', '56.g1.a1', '56.t1.a1', '56.bg1.a1', '56.bg1.b1', '56.bh1.a1'], 'contains': ['224.a1.a1', '336.h1.a1'], 'core': '112.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [562, 672, 448], 'label': '1344.8544.112.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.f1.a1', 'normal_contained_in': ['16.f1.a1', '56.c1.a1', '56.d1.a1', '56.g1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.a1.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: 74052048
    {'ambient': '1344.8544', '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': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '56.c1.a1', '56.e1.a1', '56.f1.a1', '56.v1.a1', '56.y1.a1', '56.bi1.a1', '56.bi1.b1'], 'contains': ['224.a1.a1', '336.i1.a1'], 'core': '112.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 672, 448], 'label': '1344.8544.112.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.g1.a1', 'normal_contained_in': ['16.g1.a1', '56.c1.a1', '56.e1.a1', '56.f1.a1'], 'normal_contains': ['224.a1.a1'], 'normalizer': '1.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: 74052049
    {'ambient': '1344.8544', '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.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '56.j1.a1', '56.n1.a1', '56.q1.a1', '56.t1.a1', '56.u1.a1', '56.v1.a1', '56.w1.a1'], 'contains': ['224.a1.a1', '224.e1.a1', '336.f1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [6, 672, 448], 'label': '1344.8544.112.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.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: 74052050
    {'ambient': '1344.8544', '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.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '56.k1.a1', '56.n1.a1', '56.r1.a1', '56.t1.a1', '56.x1.a1', '56.y1.a1', '56.z1.a1'], 'contains': ['224.a1.a1', '224.f1.a1', '336.g1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [4, 672, 448], 'label': '1344.8544.112.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.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: 74052051
    {'ambient': '1344.8544', '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.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '56.l1.a1', '56.o1.a1', '56.s1.a1', '56.ba1.a1', '56.be1.a1', '56.bg1.a1', '56.bi1.a1'], 'contains': ['224.a1.a1', '336.j1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [751, 448, 672], 'label': '1344.8544.112.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.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: 74052052
    {'ambient': '1344.8544', '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.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '56.l1.a1', '56.o1.b1', '56.s1.b1', '56.ba1.b1', '56.be1.a1', '56.bg1.b1', '56.bi1.b1'], 'contains': ['224.a1.a1', '336.j1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [750, 448, 672], 'label': '1344.8544.112.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '112.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052053
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.b1'], 'contains': ['8.i1.a1', '8.l1.a1', '8.n1.b1', '12.bb1.a1', '28.ba1.a1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 336, 672, 4, 448], 'label': '1344.8544.4.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.b1'], 'normal_contains': ['8.i1.a1', '8.l1.a1', '8.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052054
    {'ambient': '1344.8544', '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': '56.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '56.j1.a1', '56.p1.a1', '56.r1.a1', '56.u1.a1', '56.y1.a1', '56.bb1.a1', '56.bh1.a1'], 'contains': ['224.a1.a1', '336.k1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [7, 448, 672], 'label': '1344.8544.112.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.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: 74052055
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '112.l1', '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': ['16.l1.a1', '56.m1.a1', '56.o1.a1', '56.s1.b1', '56.bc1.a1', '56.bf1.a1', '56.bg1.a1', '56.bi1.b1'], 'contains': ['224.a1.a1', '336.l1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [205, 672, 448], 'label': '1344.8544.112.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '112.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052056
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '112.l1', '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': ['16.l1.b1', '56.m1.a1', '56.o1.b1', '56.s1.a1', '56.bc1.b1', '56.bf1.a1', '56.bg1.b1', '56.bi1.a1'], 'contains': ['224.a1.a1', '336.l1.b1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [204, 672, 448], 'label': '1344.8544.112.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '112.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052057
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '112.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '56.k1.a1', '56.p1.a1', '56.q1.a1', '56.v1.a1', '56.x1.a1', '56.bd1.a1', '56.bh1.a1'], 'contains': ['224.a1.a1', '336.m1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [5, 672, 448], 'label': '1344.8544.112.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052058
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '112.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '56.a1.a1'], 'contains': ['224.b1.a1', '224.c1.a1', '224.d1.a1', '336.n1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 2, 448], 'label': '1344.8544.112.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '112.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052059
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '112.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1', '56.a1.a1'], 'contains': ['224.b1.b1', '224.c1.a1', '224.d1.a1', '336.n1.b1'], 'core': '224.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 226, 448], 'label': '1344.8544.112.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '112.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052062
    {'ambient': '1344.8544', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.b1.a1', '84.a1.a1', '84.c1.a1', '84.f1.a1', '84.g1.a1', '84.h1.a1', '84.i1.a1', '84.j1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336], 'label': '1344.8544.168.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.a1.a1', '56.b1.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: 74052063
    {'ambient': '1344.8544', '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': '4.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '56.h1.a1', '84.a1.a1', '84.p1.a1', '84.v1.a1', '84.x1.b1', '84.ba1.b1', '84.bb1.a1', '84.be1.a1'], 'contains': ['336.b1.a1'], 'core': '168.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168], 'label': '1344.8544.168.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.b1.a1', 'normal_contained_in': ['24.e1.a1', '56.h1.a1', '84.a1.a1'], 'normal_contains': ['336.b1.a1'], 'normalizer': '1.a1.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: 74052064
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.b1', '2.k1.a1'], 'contains': ['8.i1.a1', '8.l1.b1', '8.n1.a1', '12.bb1.b1', '28.ba1.b1'], 'core': '4.s1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 192, 336, 672, 168, 448], 'label': '1344.8544.4.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.b1', 'normal_contained_in': ['2.g1.a1', '2.h1.b1', '2.k1.a1'], 'normal_contains': ['8.i1.a1', '8.l1.b1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052065
    {'ambient': '1344.8544', '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': '4.k1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '56.h1.b1', '84.a1.a1', '84.p1.b1', '84.v1.b1', '84.x1.a1', '84.ba1.a1', '84.bb1.b1', '84.be1.b1'], 'contains': ['336.b1.a1'], 'core': '168.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169], 'label': '1344.8544.168.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.b1.b1', 'normal_contained_in': ['24.e1.b1', '56.h1.b1', '84.a1.a1'], 'normal_contains': ['336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052066
    {'ambient': '1344.8544', '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': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '56.a1.a1', '84.b1.a1', '84.c1.a1', '84.d1.a1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.e1.a1', '336.n1.a1', '336.n1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [337, 2, 672], 'label': '1344.8544.168.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74052067
    {'ambient': '1344.8544', '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.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '56.j1.a1', '84.b1.a1', '84.e1.a1', '84.f1.a1'], 'contains': ['336.a1.a1', '336.f1.a1', '336.k1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 6], 'label': '1344.8544.168.d1.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.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: 74052068
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '56.k1.a1', '84.b1.a1', '84.e1.a1', '84.g1.a1'], 'contains': ['336.a1.a1', '336.g1.a1', '336.m1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [337, 4], 'label': '1344.8544.168.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.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: 74052069
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '56.c1.a1', '84.c1.a1', '84.e1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.h1.a1', '336.i1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [337, 562], 'label': '1344.8544.168.f1.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.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: 74052070
    {'ambient': '1344.8544', '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': '28.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '56.l1.a1', '84.d1.a1', '84.h1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.j1.a1', '336.j1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [337, 750], 'label': '1344.8544.168.g1.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.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: 74052071
    {'ambient': '1344.8544', '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': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '56.m1.a1', '84.d1.a1', '84.i1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.l1.a1', '336.l1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [337, 204], 'label': '1344.8544.168.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.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: 74052072
    {'ambient': '1344.8544', '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': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '56.n1.a1', '84.b1.a1', '84.l1.a1', '84.m1.a1'], 'contains': ['336.d1.a1', '336.f1.a1', '336.g1.a1', '336.o1.a1', '336.o1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [2, 4, 672], 'label': '1344.8544.168.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.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: 74052073
    {'ambient': '1344.8544', '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': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '56.d1.a1', '84.c1.a1', '84.m1.a1', '84.n1.a1', '84.n1.b1', '84.o1.a1', '84.p1.a1', '84.p1.b1'], 'contains': ['336.b1.a1', '336.d1.a1', '336.h1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 336], 'label': '1344.8544.168.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.d1.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: 74052074
    {'ambient': '1344.8544', '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': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '56.e1.a1', '84.c1.a1', '84.l1.a1', '84.q1.a1'], 'contains': ['336.c1.a1', '336.d1.a1', '336.i1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 2], 'label': '1344.8544.168.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74052075
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1', '336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.j1.a1', '8.k1.a1', '8.n1.a1', '12.e1.a1', '28.bb1.a1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 192, 448, 1008, 168, 672], 'label': '1344.8544.4.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.d1.a1', '2.i1.a1', '2.k1.a1'], 'normal_contains': ['8.j1.a1', '8.k1.a1', '8.n1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052076
    {'ambient': '1344.8544', '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': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '56.o1.a1', '84.d1.a1', '84.n1.a1', '84.q1.a1'], 'contains': ['336.d1.a1', '336.j1.a1', '336.l1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [653, 2], 'label': '1344.8544.168.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.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: 74052077
    {'ambient': '1344.8544', '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': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.b1', '56.o1.b1', '84.d1.a1', '84.n1.b1', '84.q1.a1'], 'contains': ['336.d1.a1', '336.j1.b1', '336.l1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [898, 204], 'label': '1344.8544.168.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.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: 74052078
    {'ambient': '1344.8544', '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': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '56.p1.a1', '84.b1.a1', '84.l1.a1', '84.o1.a1'], 'contains': ['336.d1.a1', '336.k1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [5, 2], 'label': '1344.8544.168.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.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: 74052079
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '56.q1.a1', '84.b1.a1', '84.r1.a1', '84.s1.a1'], 'contains': ['336.e1.a1', '336.f1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1237, 6], 'label': '1344.8544.168.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.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: 74052080
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '56.r1.a1', '84.b1.a1', '84.r1.a1', '84.t1.a1'], 'contains': ['336.e1.a1', '336.g1.a1', '336.k1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [339, 4], 'label': '1344.8544.168.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.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: 74052081
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '56.f1.a1', '84.c1.a1', '84.s1.a1', '84.t1.a1', '84.u1.a1', '84.u1.b1', '84.v1.a1', '84.v1.b1'], 'contains': ['336.b1.a1', '336.e1.a1', '336.i1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 336], 'label': '1344.8544.168.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.f1.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: 74052082
    {'ambient': '1344.8544', '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': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '56.g1.a1', '84.c1.a1', '84.r1.a1', '84.w1.a1'], 'contains': ['336.c1.a1', '336.e1.a1', '336.h1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 562], 'label': '1344.8544.168.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.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: 74052083
    {'ambient': '1344.8544', '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': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '56.s1.a1', '84.d1.a1', '84.u1.a1', '84.w1.a1'], 'contains': ['336.e1.a1', '336.j1.a1', '336.l1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1235, 204], 'label': '1344.8544.168.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.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: 74052084
    {'ambient': '1344.8544', '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': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.b1', '56.s1.b1', '84.d1.a1', '84.u1.b1', '84.w1.a1'], 'contains': ['336.e1.a1', '336.j1.b1', '336.l1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [861, 750], 'label': '1344.8544.168.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052085
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '56.t1.a1', '84.e1.a1', '84.m1.a1', '84.r1.a1'], 'contains': ['336.f1.a1', '336.g1.a1', '336.h1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1010, 4], 'label': '1344.8544.168.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.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: 74052086
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1', '336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.b1', '2.k1.b1'], 'contains': ['8.j1.b1', '8.k1.a1', '8.n1.b1', '12.e1.b1', '28.bb1.b1'], 'core': '4.t1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 448, 336, 750, 672], 'label': '1344.8544.4.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.b1', 'normal_contained_in': ['2.d1.a1', '2.i1.b1', '2.k1.b1'], 'normal_contains': ['8.j1.b1', '8.k1.a1', '8.n1.b1', '12.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052087
    {'ambient': '1344.8544', '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': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '56.u1.a1', '84.f1.a1', '84.l1.a1', '84.r1.a1'], 'contains': ['336.c1.a1', '336.f1.a1', '336.k1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 6], 'label': '1344.8544.168.t1.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.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: 74052088
    {'ambient': '1344.8544', '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': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '56.v1.a1', '84.e1.a1', '84.l1.a1', '84.s1.a1'], 'contains': ['336.f1.a1', '336.i1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [5, 6], 'label': '1344.8544.168.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.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: 74052089
    {'ambient': '1344.8544', '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': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.w1.a1', '84.f1.a1', '84.m1.a1', '84.s1.a1', '84.x1.a1', '84.x1.b1', '84.y1.a1', '84.y1.b1'], 'contains': ['336.b1.a1', '336.f1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [6, 336], 'label': '1344.8544.168.v1.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.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: 74052090
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '56.x1.a1', '84.g1.a1', '84.l1.a1', '84.r1.a1'], 'contains': ['336.c1.a1', '336.g1.a1', '336.m1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 4], 'label': '1344.8544.168.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052091
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '56.y1.a1', '84.e1.a1', '84.l1.a1', '84.t1.a1'], 'contains': ['336.g1.a1', '336.i1.a1', '336.k1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [3, 4], 'label': '1344.8544.168.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052092
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '56.z1.a1', '84.g1.a1', '84.m1.a1', '84.t1.a1', '84.z1.a1', '84.z1.b1', '84.ba1.a1', '84.ba1.b1'], 'contains': ['336.b1.a1', '336.g1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [4, 336], 'label': '1344.8544.168.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052093
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.ba1.a1', '84.h1.a1', '84.n1.a1', '84.u1.a1', '84.x1.a1', '84.z1.a1', '84.bb1.a1', '84.bc1.a1'], 'contains': ['336.b1.a1', '336.j1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [751, 336], 'label': '1344.8544.168.z1.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.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052094
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '56.ba1.b1', '84.h1.a1', '84.n1.b1', '84.u1.b1', '84.x1.b1', '84.z1.b1', '84.bb1.b1', '84.bc1.b1'], 'contains': ['336.b1.a1', '336.j1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [750, 336], 'label': '1344.8544.168.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052095
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '56.bb1.a1', '84.f1.a1', '84.o1.a1', '84.t1.a1', '84.bb1.a1', '84.bb1.b1', '84.bd1.a1', '84.bd1.b1'], 'contains': ['336.b1.a1', '336.k1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [7, 336], 'label': '1344.8544.168.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052096
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bb1', '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.bb1.a1', '56.bc1.a1', '84.i1.a1', '84.n1.a1', '84.u1.b1', '84.y1.a1', '84.ba1.a1', '84.bd1.a1', '84.be1.a1'], 'contains': ['336.b1.a1', '336.l1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [205, 336], 'label': '1344.8544.168.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052097
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1', '336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.j1.a1', '8.m1.a1', '8.o1.a1', '12.bc1.a1', '28.bc1.a1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 1008, 672, 58, 448], 'label': '1344.8544.4.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.j1.a1'], 'normal_contains': ['8.j1.a1', '8.m1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052098
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bb1', '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.bb1.b1', '56.bc1.b1', '84.i1.a1', '84.n1.b1', '84.u1.a1', '84.y1.b1', '84.ba1.b1', '84.bd1.b1', '84.be1.b1'], 'contains': ['336.b1.a1', '336.l1.b1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [204, 336], 'label': '1344.8544.168.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052099
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '56.bd1.a1', '84.g1.a1', '84.o1.a1', '84.s1.a1', '84.bc1.a1', '84.bc1.b1', '84.be1.a1', '84.be1.b1'], 'contains': ['336.b1.a1', '336.m1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': None, 'generators': [5, 336], 'label': '1344.8544.168.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052100
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '56.i1.a1', '84.j1.a1', '84.p1.a1', '84.v1.b1', '84.y1.b1', '84.z1.b1', '84.bc1.a1', '84.bd1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [58], 'label': '1344.8544.168.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052101
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.b1', '56.i1.b1', '84.j1.a1', '84.p1.b1', '84.v1.a1', '84.y1.a1', '84.z1.a1', '84.bc1.b1', '84.bd1.b1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [59], 'label': '1344.8544.168.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052102
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '56.be1.a1', '84.h1.a1', '84.q1.a1', '84.w1.a1'], 'contains': ['336.c1.a1', '336.j1.a1', '336.j1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [1, 750], 'label': '1344.8544.168.be1.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.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052103
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bf1', '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.bf1.a1', '56.bf1.a1', '84.i1.a1', '84.q1.a1', '84.w1.a1'], 'contains': ['336.c1.a1', '336.l1.a1', '336.l1.b1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [1, 204], 'label': '1344.8544.168.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052104
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bg1', '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.bg1.a1', '56.bg1.a1', '84.k1.a1', '84.n1.a1', '84.w1.a1'], 'contains': ['336.h1.a1', '336.j1.a1', '336.l1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [205, 562], 'label': '1344.8544.168.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052105
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bg1', '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.bg1.b1', '56.bg1.b1', '84.k1.a1', '84.n1.b1', '84.w1.a1'], 'contains': ['336.h1.a1', '336.j1.b1', '336.l1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [562, 204], 'label': '1344.8544.168.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052106
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '56.bh1.a1', '84.e1.a1', '84.o1.a1', '84.r1.a1'], 'contains': ['336.h1.a1', '336.k1.a1', '336.m1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [901, 562], 'label': '1344.8544.168.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052107
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bi1', '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.bi1.a1', '56.bi1.a1', '84.k1.a1', '84.q1.a1', '84.u1.a1'], 'contains': ['336.i1.a1', '336.j1.a1', '336.l1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [899, 204], 'label': '1344.8544.168.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052108
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1', '336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.b1', '2.j1.b1'], 'contains': ['8.j1.b1', '8.m1.a1', '8.o1.b1', '12.bc1.b1', '28.bc1.b1'], 'core': '4.u1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 336, 672, 750, 448], 'label': '1344.8544.4.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.b1', 'normal_contained_in': ['2.f1.a1', '2.i1.b1', '2.j1.b1'], 'normal_contains': ['8.j1.b1', '8.m1.a1', '8.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052109
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '168.bi1', '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.bi1.b1', '56.bi1.b1', '84.k1.a1', '84.q1.a1', '84.u1.b1'], 'contains': ['336.i1.a1', '336.j1.b1', '336.l1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [973, 750], 'label': '1344.8544.168.bi1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '168.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052110
    {'ambient': '1344.8544', '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.c1.b1', '96.d1.a1', '96.e1.a1', '96.f1.a1'], 'contains': ['1344.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [192], 'label': '1344.8544.192.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: 74052111
    {'ambient': '1344.8544', '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.j1.a1', '112.j1.b1', '112.k1.a1', '112.l1.a1', '112.l1.b1', '112.m1.a1'], 'contains': ['448.a1.a1', '672.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672, 448], 'label': '1344.8544.224.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.a1.a1', 'normal_contained_in': ['32.a1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1', '112.e1.a1', '112.d1.a1', '112.g1.a1', '112.f1.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: 74052112
    {'ambient': '1344.8544', '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': '6.a1.a1', 'complements': ['6.g1.a1', '6.k1.a1', '6.a1.a1', '6.j1.b1', '6.f1.a1', '6.k1.b1', '6.e1.a1', '6.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '112.b1.a1', '112.n1.a1', '112.o1.a1'], 'contains': ['448.a1.a1', '672.c1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 448], 'label': '1344.8544.224.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.b1.a1', 'normal_contained_in': ['32.b1.a1', '112.b1.a1'], 'normal_contains': ['448.a1.a1'], 'normalizer': '1.a1.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: 74052113
    {'ambient': '1344.8544', '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': '6.a1.a1', 'complements': ['6.g1.a1', '6.k1.a1', '6.a1.a1', '6.j1.b1', '6.f1.a1', '6.k1.b1', '6.e1.a1', '6.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '112.b1.a1', '112.n1.b1', '112.o1.b1'], 'contains': ['448.a1.a1', '672.c1.b1'], 'core': '224.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [226, 448], 'label': '1344.8544.224.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.b1.b1', 'normal_contained_in': ['32.b1.b1', '112.b1.a1'], 'normal_contains': ['448.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052114
    {'ambient': '1344.8544', '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': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '112.a1.a1', '112.n1.a1', '112.n1.b1'], 'contains': ['448.a1.a1', '672.b1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 448], 'label': '1344.8544.224.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74052115
    {'ambient': '1344.8544', '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': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '112.c1.a1', '112.n1.a1', '112.n1.b1'], 'contains': ['448.a1.a1', '672.d1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1235, 448], 'label': '1344.8544.224.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74052116
    {'ambient': '1344.8544', '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.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '112.h1.a1', '112.o1.a1', '112.o1.b1'], 'contains': ['448.a1.a1', '672.e1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [6, 448], 'label': '1344.8544.224.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.n1.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: 74052117
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '224.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '112.i1.a1', '112.o1.a1', '112.o1.b1'], 'contains': ['448.a1.a1', '672.f1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [4, 448], 'label': '1344.8544.224.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.n1.a1', 'old_label': '224.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052118
    {'ambient': '1344.8544', '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.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.c1.a1', '168.d1.a1', '168.e1.a1', '168.f1.a1', '168.g1.a1', '168.h1.a1'], 'contains': ['672.a1.a1', '672.b1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [337, 672], 'label': '1344.8544.336.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: 74052119
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1', '336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.a1', '2.k1.b1'], 'contains': ['8.k1.a1', '8.l1.a1', '8.o1.a1', '12.bd1.a1', '28.bd1.a1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [205, 192, 336, 672, 58, 448], 'label': '1344.8544.4.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.e1.a1', '2.i1.a1', '2.k1.b1'], 'normal_contains': ['8.k1.a1', '8.l1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052120
    {'ambient': '1344.8544', '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.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '112.d1.a1', '168.a1.a1', '168.b1.a1', '168.b1.b1', '168.j1.a1', '168.p1.a1', '168.v1.a1', '168.y1.a1', '168.z1.a1', '168.z1.b1', '168.ba1.a1', '168.bb1.a1', '168.bb1.b1', '168.bc1.a1', '168.bd1.a1', '168.bd1.b1'], 'contains': ['672.a1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [336], 'label': '1344.8544.336.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.b1.a1', 'normal_contained_in': ['48.b1.a1', '112.d1.a1', '168.a1.a1', '168.b1.a1', '168.b1.b1'], '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: 74052121
    {'ambient': '1344.8544', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '112.e1.a1', '168.a1.a1', '168.k1.a1', '168.q1.a1', '168.t1.a1', '168.w1.a1', '168.be1.a1', '168.bf1.a1'], 'contains': ['672.a1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1], 'label': '1344.8544.336.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.c1.a1', 'normal_contained_in': ['48.c1.a1', '112.e1.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: 74052122
    {'ambient': '1344.8544', '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': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '112.b1.a1', '168.c1.a1', '168.i1.a1', '168.j1.a1', '168.k1.a1', '168.l1.a1', '168.l1.b1', '168.m1.a1'], 'contains': ['672.a1.a1', '672.c1.a1', '672.c1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 672], 'label': '1344.8544.336.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74052123
    {'ambient': '1344.8544', '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': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '112.c1.a1', '168.c1.a1', '168.n1.a1', '168.o1.a1', '168.p1.a1', '168.q1.a1', '168.r1.a1', '168.r1.b1'], 'contains': ['672.a1.a1', '672.d1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1235, 672], 'label': '1344.8544.336.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74052124
    {'ambient': '1344.8544', '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': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '112.h1.a1', '168.d1.a1', '168.i1.a1', '168.n1.a1', '168.s1.a1', '168.t1.a1', '168.u1.a1', '168.v1.a1'], 'contains': ['672.a1.a1', '672.e1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [6, 672], 'label': '1344.8544.336.f1.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.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: 74052125
    {'ambient': '1344.8544', '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': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '112.i1.a1', '168.e1.a1', '168.i1.a1', '168.o1.a1', '168.s1.a1', '168.w1.a1', '168.x1.a1', '168.y1.a1'], 'contains': ['672.a1.a1', '672.f1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [4, 672], 'label': '1344.8544.336.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.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: 74052126
    {'ambient': '1344.8544', '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': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '112.f1.a1', '168.f1.a1', '168.j1.a1', '168.q1.a1', '168.s1.a1', '168.bg1.a1', '168.bg1.b1', '168.bh1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [562], 'label': '1344.8544.336.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74052127
    {'ambient': '1344.8544', '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': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '112.g1.a1', '168.f1.a1', '168.k1.a1', '168.p1.a1', '168.u1.a1', '168.x1.a1', '168.bi1.a1', '168.bi1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3], 'label': '1344.8544.336.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.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: 74052128
    {'ambient': '1344.8544', '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': '28.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '112.j1.a1', '168.g1.a1', '168.l1.a1', '168.r1.a1', '168.z1.a1', '168.be1.a1', '168.bg1.a1', '168.bi1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [751], 'label': '1344.8544.336.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.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: 74052129
    {'ambient': '1344.8544', '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': '28.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.b1', '112.j1.b1', '168.g1.a1', '168.l1.b1', '168.r1.b1', '168.z1.b1', '168.be1.a1', '168.bg1.b1', '168.bi1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [750], 'label': '1344.8544.336.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '336.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052130
    {'ambient': '1344.8544', '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.f1.a1', '672.c1.a1', '672.c1.b1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '4.p1.a1', '4.p1.b1', '4.t1.a1', '4.t1.b1', '6.a1.a1', '14.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 672, 168, 448, 6, 192, 336], 'label': '1344.8544.2.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.d1.a1', '4.f1.a1', '4.p1.a1', '4.p1.b1', '4.t1.a1', '4.t1.b1', '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: 74052131
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1', '336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.b1', '2.k1.a1'], 'contains': ['8.k1.a1', '8.l1.b1', '8.o1.b1', '12.bd1.b1', '28.bd1.b1'], 'core': '4.v1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [59, 192, 1008, 672, 204, 448], 'label': '1344.8544.4.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.b1', 'normal_contained_in': ['2.e1.a1', '2.i1.b1', '2.k1.a1'], 'normal_contains': ['8.k1.a1', '8.l1.b1', '8.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052132
    {'ambient': '1344.8544', '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': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '112.k1.a1', '168.d1.a1', '168.m1.a1', '168.o1.a1', '168.t1.a1', '168.x1.a1', '168.ba1.a1', '168.bh1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': None, 'generators': [7], 'label': '1344.8544.336.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.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: 74052133
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '112.l1.a1', '168.h1.a1', '168.l1.a1', '168.r1.b1', '168.bb1.a1', '168.bf1.a1', '168.bg1.a1', '168.bi1.b1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [205], 'label': '1344.8544.336.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '336.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052134
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.b1', '112.l1.b1', '168.h1.a1', '168.l1.b1', '168.r1.a1', '168.bb1.b1', '168.bf1.a1', '168.bg1.b1', '168.bi1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [204], 'label': '1344.8544.336.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.b1.a1', 'old_label': '336.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052135
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '112.m1.a1', '168.e1.a1', '168.m1.a1', '168.n1.a1', '168.u1.a1', '168.w1.a1', '168.bc1.a1', '168.bh1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': None, 'generators': [5], 'label': '1344.8544.336.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '336.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052136
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '336.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '112.n1.a1', '168.c1.a1'], 'contains': ['672.b1.a1', '672.c1.a1', '672.d1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 2], 'label': '1344.8544.336.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '336.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052137
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '336.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.b1', '112.n1.b1', '168.c1.a1'], 'contains': ['672.b1.a1', '672.c1.b1', '672.d1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [337, 226], 'label': '1344.8544.336.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '56.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '336.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052138
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '336.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '112.o1.a1', '168.i1.a1'], 'contains': ['672.c1.a1', '672.e1.a1', '672.f1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': None, 'generators': [2, 4], 'label': '1344.8544.336.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.l1.a1', 'old_label': '336.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052139
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '336.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.b1', '112.o1.b1', '168.i1.a1'], 'contains': ['672.c1.b1', '672.e1.a1', '672.f1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': None, 'generators': [674, 4], 'label': '1344.8544.336.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.l1.a1', 'old_label': '336.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052159
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.be1', '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.b1.a1'], 'contains': ['8.g1.a1', '8.y1.a1', '8.y1.b1', '8.be1.a1', '8.bf1.a1', '8.bg1.a1', '8.bg1.b1', '12.y1.a1', '28.w1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 204, 672, 562, 448], 'label': '1344.8544.4.be1.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.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052140
    {'ambient': '1344.8544', '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.b1.b1', '224.c1.a1', '224.d1.a1', '224.e1.a1', '224.f1.a1'], 'contains': ['1344.a1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [448], 'label': '1344.8544.448.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '448.a1.a1', 'normal_contained_in': ['64.a1.a1', '224.a1.a1', '224.b1.b1', '224.b1.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: 74052141
    {'ambient': '1344.8544', '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.j1.a1', '336.j1.b1', '336.k1.a1', '336.l1.a1', '336.l1.b1', '336.m1.a1'], 'contains': ['1344.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [672], 'label': '1344.8544.672.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: 74052142
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1', '336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.b1'], 'contains': ['8.l1.a1', '8.m1.a1', '8.n1.a1', '12.be1.a1', '28.be1.a1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 192, 1008, 672, 168, 448], 'label': '1344.8544.4.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.b1'], 'normal_contains': ['8.l1.a1', '8.m1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052143
    {'ambient': '1344.8544', '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.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '224.c1.a1', '336.a1.a1', '336.n1.a1', '336.n1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337], 'label': '1344.8544.672.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '336.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74052144
    {'ambient': '1344.8544', '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': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '224.b1.a1', '336.d1.a1', '336.n1.a1', '336.o1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2], 'label': '1344.8544.672.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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: 74052145
    {'ambient': '1344.8544', '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': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.b1', '224.b1.b1', '336.d1.a1', '336.n1.b1', '336.o1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [226], 'label': '1344.8544.672.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '672.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052146
    {'ambient': '1344.8544', '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': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '224.d1.a1', '336.e1.a1', '336.n1.a1', '336.n1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1235], 'label': '1344.8544.672.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '112.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.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: 74052147
    {'ambient': '1344.8544', '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': '28.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '224.e1.a1', '336.f1.a1', '336.o1.a1', '336.o1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': None, 'generators': [6], 'label': '1344.8544.672.e1.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.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: 74052148
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '672.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '224.f1.a1', '336.g1.a1', '336.o1.a1', '336.o1.b1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': None, 'generators': [4], 'label': '1344.8544.672.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.l1.a1', 'old_label': '672.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052149
    {'ambient': '1344.8544', '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.c1.b1', '672.d1.a1', '672.e1.a1', '672.f1.a1'], 'contains': [], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '1344.8544.1344.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: 74052150
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['336.o1.a1', '336.o1.b1', '336.n1.a1', '336.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.b1', '2.j1.a1'], 'contains': ['8.l1.b1', '8.m1.a1', '8.n1.b1', '12.be1.b1', '28.be1.b1'], 'core': '4.w1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 336, 672, 204, 448], 'label': '1344.8544.4.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': ['2.g1.a1', '2.i1.b1', '2.j1.a1'], 'normal_contains': ['8.l1.b1', '8.m1.a1', '8.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052151
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.p1.a1', '8.q1.a1', '8.t1.a1', '8.v1.a1', '8.w1.a1', '8.x1.a1', '12.f1.a1', '28.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 192, 4, 672, 2, 448], 'label': '1344.8544.4.x1.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.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052152
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.y1', '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.b1.a1'], 'contains': ['8.a1.a1', '8.r1.a1', '8.s1.a1', '8.u1.a1', '8.u1.b1', '8.y1.a1', '8.y1.b1', '12.h1.a1', '28.g1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 192, 204, 672, 2, 448], 'label': '1344.8544.4.y1.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.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052153
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.p1.a1', '8.q1.a1', '8.z1.a1', '8.bb1.a1', '8.bd1.a1', '8.bh1.a1', '12.i1.a1', '28.h1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 192, 4, 672, 562, 448], 'label': '1344.8544.4.z1.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.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052154
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.ba1', '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.b1.a1'], 'contains': ['8.c1.a1', '8.r1.a1', '8.s1.a1', '8.bg1.a1', '8.bg1.b1', '8.bi1.a1', '8.bi1.b1', '12.m1.a1', '28.m1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 192, 204, 672, 562, 448], 'label': '1344.8544.4.ba1.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.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052155
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.e1.a1', '8.t1.a1', '8.v1.a1', '8.ba1.a1', '8.bb1.a1', '8.bc1.a1', '8.bd1.a1', '12.n1.a1', '28.n1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 4, 672, 2, 448], 'label': '1344.8544.4.bb1.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.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052156
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.bc1', '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.b1.a1'], 'contains': ['8.e1.a1', '8.u1.a1', '8.u1.b1', '8.be1.a1', '8.bf1.a1', '8.bi1.a1', '8.bi1.b1', '12.s1.a1', '28.r1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 204, 672, 2, 448], 'label': '1344.8544.4.bc1.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.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052157
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '4.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.g1.a1', '8.w1.a1', '8.x1.a1', '8.z1.a1', '8.ba1.a1', '8.bc1.a1', '8.bh1.a1', '12.t1.a1', '28.s1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 192, 4, 672, 562, 448], 'label': '1344.8544.4.bd1.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.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052158
    {'ambient': '1344.8544', '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': '672.a1.a1', 'complements': ['672.f1.a1', '672.c1.a1', '672.c1.b1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '4.q1.a1', '4.q1.b1', '4.v1.a1', '4.v1.b1', '6.e1.a1', '14.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 204, 1008, 58, 192, 672], 'label': '1344.8544.2.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.e1.a1', '4.g1.a1', '4.q1.a1', '4.q1.b1', '4.v1.a1', '4.v1.b1'], '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: 74052160
    {'ambient': '1344.8544', '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': '112.b1.a1', 'complements': ['224.f1.a1', '224.b1.a1', '224.b1.b1', '224.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.e1.a1', '12.e1.b1', '42.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 168, 336, 6, 672], 'label': '1344.8544.6.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', '12.d1.a1', '12.d1.b1', '12.e1.a1', '12.e1.b1'], '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: 74052161
    {'ambient': '1344.8544', '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': '168.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.a1', '12.g1.a1', '12.i1.a1', '12.j1.a1', '12.n1.a1', '12.o1.a1', '12.q1.a1', '12.t1.a1', '12.u1.a1', '12.v1.a1', '42.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 4, 336, 2, 672], 'label': '1344.8544.6.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: 74052162
    {'ambient': '1344.8544', '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': '168.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.g1.a1', '12.h1.a1', '12.k1.a1', '12.m1.a1', '12.p1.a1', '12.p1.b1', '12.s1.a1', '12.w1.a1', '12.w1.b1', '12.y1.a1', '42.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 204, 336, 898, 672], 'label': '1344.8544.6.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: 74052163
    {'ambient': '1344.8544', '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': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.g1.a1', '12.l1.a1', '12.r1.a1', '12.r1.b1', '12.x1.a1', '12.x1.b1', '42.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 672, 168, 192, 2, 336], 'label': '1344.8544.6.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: 74052164
    {'ambient': '1344.8544', '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.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.k1.a1', '12.l1.a1', '12.z1.a1', '12.z1.b1', '12.bd1.a1', '12.bd1.b1', '42.e1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 204, 1008, 58, 672], 'label': '1344.8544.6.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: 74052165
    {'ambient': '1344.8544', '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.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.j1.a1', '12.l1.a1', '12.ba1.a1', '12.ba1.b1', '12.bc1.a1', '12.bc1.b1', '42.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 4, 1008, 506, 672], 'label': '1344.8544.6.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: 74052166
    {'ambient': '1344.8544', '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': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.j1.a1', '12.k1.a1', '12.bb1.a1', '12.bb1.b1', '12.be1.a1', '12.be1.b1', '42.g1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 192, 168, 336, 4, 672], 'label': '1344.8544.6.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: 74052167
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '6.h1', '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': ['2.h1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.o1.a1', '12.p1.a1', '12.r1.b1', '12.z1.a1', '12.ba1.a1', '12.bb1.a1', '42.h1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 4, 336, 2, 672], 'label': '1344.8544.6.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052168
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '6.h1', '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': ['2.h1.b1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.o1.a1', '12.p1.b1', '12.r1.a1', '12.z1.b1', '12.ba1.b1', '12.bb1.b1', '42.h1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2, 192, 168, 336, 4, 672], 'label': '1344.8544.6.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052169
    {'ambient': '1344.8544', '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': '672.a1.a1', 'complements': ['672.c1.a1', '672.c1.b1', '672.e1.a1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '4.r1.a1', '4.r1.b1', '4.u1.a1', '4.u1.b1', '6.f1.a1', '14.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 4, 1008, 58, 192, 672], 'label': '1344.8544.2.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.g1.a1', '4.r1.a1', '4.r1.b1', '4.u1.a1', '4.u1.b1'], '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: 74052170
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '6.i1', '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': ['2.i1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.p1.a1', '12.q1.a1', '12.r1.a1', '12.bc1.a1', '12.bd1.a1', '12.be1.a1', '42.i1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 192, 168, 1008, 2, 672], 'label': '1344.8544.6.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052171
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '6.i1', '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': ['2.i1.b1', '3.a1.a1'], 'contains': ['12.e1.b1', '12.p1.b1', '12.q1.a1', '12.r1.b1', '12.bc1.b1', '12.bd1.b1', '12.be1.b1', '42.i1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 204, 336, 898, 672], 'label': '1344.8544.6.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052172
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '6.j1', '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': ['2.j1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.u1.a1', '12.w1.a1', '12.x1.b1', '12.z1.b1', '12.bc1.a1', '12.be1.b1', '42.j1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 204, 336, 58, 672], 'label': '1344.8544.6.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052173
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '6.j1', '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': ['2.j1.b1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.u1.a1', '12.w1.b1', '12.x1.a1', '12.z1.a1', '12.bc1.b1', '12.be1.a1', '42.j1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [5, 192, 168, 1008, 6, 672], 'label': '1344.8544.6.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052174
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '6.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': ['2.k1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.v1.a1', '12.w1.a1', '12.x1.a1', '12.ba1.a1', '12.bb1.b1', '12.bd1.b1', '42.k1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [3, 192, 168, 336, 4, 672], 'label': '1344.8544.6.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052175
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '6.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': ['2.k1.b1', '3.a1.a1'], 'contains': ['12.e1.b1', '12.v1.a1', '12.w1.b1', '12.x1.b1', '12.ba1.b1', '12.bb1.a1', '12.bd1.a1', '42.k1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [169, 192, 4, 336, 506, 672], 'label': '1344.8544.6.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052176
    {'ambient': '1344.8544', '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', '14.h1.a1', '14.h1.b1', '14.i1.a1', '14.i1.b1', '14.j1.a1', '14.j1.b1', '14.k1.a1', '14.k1.b1', '21.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': None, 'generators': [1, 672, 336, 2, 448, 4, 168], 'label': '1344.8544.7.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: 74052177
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.a1', '4.y1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.n1.a1', '16.n1.b1', '24.f1.a1', '56.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [337, 672, 192, 2, 448], 'label': '1344.8544.8.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.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: 74052193
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.l1.a1', '4.u1.a1', '4.u1.b1', '4.w1.a1', '4.w1.b1'], 'contains': ['16.d1.a1', '16.m1.a1', '24.bc1.a1', '56.bd1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5, 672, 448, 336, 192], 'label': '1344.8544.8.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.c1.a1', '4.j1.a1', '4.l1.a1', '4.u1.a1', '4.u1.b1', '4.w1.a1', '4.w1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.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: 74052178
    {'ambient': '1344.8544', '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': '8.b1.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.d1.a1', '16.e1.a1', '24.a1.a1', '56.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 192, 336, 672], 'label': '1344.8544.8.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.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.e1.a1', '16.d1.a1', '24.a1.a1', '56.b1.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: 74052179
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.z1.a1', '4.ba1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.g1.a1', '24.i1.a1', '56.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [337, 192, 672, 562, 448], 'label': '1344.8544.8.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.g1.a1', '16.f1.a1', '56.c1.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: 74052180
    {'ambient': '1344.8544', '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.c1.a1', '672.c1.b1', '672.e1.a1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '4.s1.a1', '4.s1.b1', '4.w1.a1', '4.w1.b1', '6.g1.a1', '14.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 168, 336, 4, 192, 672], 'label': '1344.8544.2.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '4.s1.a1', '4.s1.b1', '4.w1.a1', '4.w1.b1'], '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: 74052181
    {'ambient': '1344.8544', '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': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.i1.b1', '4.j1.a1', '4.k1.a1', '4.k1.b1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.f1.a1', '24.m1.a1', '56.d1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 672, 336, 448], 'label': '1344.8544.8.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.i1.b1', '4.j1.a1', '4.k1.a1', '4.k1.b1'], 'normal_contains': ['16.b1.a1', '16.d1.a1', '16.f1.a1', '56.d1.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: 74052182
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bb1.a1', '4.bc1.a1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.g1.a1', '24.n1.a1', '56.e1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 672, 2, 448], 'label': '1344.8544.8.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1', '16.e1.a1', '16.g1.a1', '56.e1.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: 74052183
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.l1.a1', '4.m1.a1', '4.n1.a1', '4.n1.b1', '4.o1.a1', '4.o1.b1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.g1.a1', '24.s1.a1', '56.f1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 192, 672, 336, 448], 'label': '1344.8544.8.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.a1.a1', '4.l1.a1', '4.m1.a1', '4.n1.a1', '4.n1.b1', '4.o1.a1', '4.o1.b1'], 'normal_contains': ['16.c1.a1', '16.d1.a1', '16.g1.a1', '56.f1.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: 74052184
    {'ambient': '1344.8544', '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': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bd1.a1', '4.be1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '16.f1.a1', '24.t1.a1', '56.g1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 192, 672, 562, 448], 'label': '1344.8544.8.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '16.e1.a1', '16.f1.a1', '56.g1.a1'], 'normalizer': '1.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: 74052185
    {'ambient': '1344.8544', '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.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.l1.a1', '4.p1.a1', '4.p1.b1', '4.q1.a1', '4.q1.b1'], 'contains': ['16.d1.a1', '16.h1.a1', '24.b1.a1', '56.w1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 448, 672, 336, 192], 'label': '1344.8544.8.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.b1.a1', '4.h1.a1', '4.l1.a1', '4.p1.a1', '4.p1.b1', '4.q1.a1', '4.q1.b1'], 'normal_contains': ['16.d1.a1', '24.b1.a1'], 'normalizer': '1.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: 74052186
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.m1.a1', '4.r1.a1', '4.r1.b1', '4.s1.a1', '4.s1.b1'], 'contains': ['16.d1.a1', '16.i1.a1', '24.ba1.a1', '56.z1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 672, 448, 336, 192], 'label': '1344.8544.8.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.c1.a1', '4.h1.a1', '4.m1.a1', '4.r1.a1', '4.r1.b1', '4.s1.a1', '4.s1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.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: 74052187
    {'ambient': '1344.8544', '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': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.n1.a1', '4.p1.a1', '4.r1.a1', '4.t1.a1', '4.u1.a1'], 'contains': ['16.d1.a1', '16.j1.a1', '24.c1.a1', '56.ba1.a1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [751, 448, 672, 336, 192], 'label': '1344.8544.8.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.d1.a1', '4.i1.a1', '4.n1.a1', '4.p1.a1', '4.r1.a1', '4.t1.a1', '4.u1.a1'], 'normal_contains': ['16.d1.a1', '24.c1.a1'], 'normalizer': '1.a1.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: 74052188
    {'ambient': '1344.8544', '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': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.b1', '4.n1.b1', '4.p1.b1', '4.r1.b1', '4.t1.b1', '4.u1.b1'], 'contains': ['16.d1.a1', '16.j1.b1', '24.c1.b1', '56.ba1.b1'], 'core': '8.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [750, 448, 672, 336, 192], 'label': '1344.8544.8.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.b1', 'normal_contained_in': ['4.d1.a1', '4.i1.b1', '4.n1.b1', '4.p1.b1', '4.r1.b1', '4.t1.b1', '4.u1.b1'], 'normal_contains': ['16.d1.a1', '24.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052189
    {'ambient': '1344.8544', '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': '112.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.m1.a1', '4.t1.a1', '4.t1.b1', '4.v1.a1', '4.v1.b1'], 'contains': ['16.d1.a1', '16.k1.a1', '24.d1.a1', '56.bb1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 448, 672, 336, 192], 'label': '1344.8544.8.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.b1.a1', '4.j1.a1', '4.m1.a1', '4.t1.a1', '4.t1.b1', '4.v1.a1', '4.v1.b1'], 'normal_contains': ['16.d1.a1', '24.d1.a1'], 'normalizer': '1.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: 74052190
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.n1.b1', '4.q1.a1', '4.s1.a1', '4.v1.a1', '4.w1.a1'], 'contains': ['16.d1.a1', '16.l1.a1', '24.bb1.a1', '56.bc1.a1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [205, 672, 448, 336, 192], 'label': '1344.8544.8.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.e1.a1', '4.i1.a1', '4.n1.b1', '4.q1.a1', '4.s1.a1', '4.v1.a1', '4.w1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.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: 74052191
    {'ambient': '1344.8544', 'aut_centralizer_order': None, 'aut_label': '2.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': ['672.b1.a1', '672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.a1', '4.k1.b1', '4.p1.a1', '4.q1.a1', '4.r1.a1', '4.s1.a1', '6.h1.a1', '14.h1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 448, 4, 336, 2, 192, 672], 'label': '1344.8544.2.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.i1.a1', '4.k1.b1', '4.p1.a1', '4.q1.a1', '4.r1.a1', '4.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052192
    {'ambient': '1344.8544', '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': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.b1', '4.n1.a1', '4.q1.b1', '4.s1.b1', '4.v1.b1', '4.w1.b1'], 'contains': ['16.d1.a1', '16.l1.b1', '24.bb1.b1', '56.bc1.b1'], 'core': '8.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [204, 672, 448, 336, 192], 'label': '1344.8544.8.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': ['4.e1.a1', '4.i1.b1', '4.n1.a1', '4.q1.b1', '4.s1.b1', '4.v1.b1', '4.w1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052194
    {'ambient': '1344.8544', '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': '8.n1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.k1.a1', '4.o1.a1', '4.p1.b1', '4.s1.b1', '4.t1.a1', '4.w1.a1'], 'contains': ['16.d1.a1', '24.e1.a1', '56.h1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [168, 192, 336, 448, 672], 'label': '1344.8544.8.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.f1.a1', '4.k1.a1', '4.o1.a1', '4.p1.b1', '4.s1.b1', '4.t1.a1', '4.w1.a1'], 'normal_contains': ['16.d1.a1', '24.e1.a1', '56.h1.a1'], 'normalizer': '1.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: 74052195
    {'ambient': '1344.8544', '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': '8.n1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.k1.b1', '4.o1.b1', '4.p1.a1', '4.s1.a1', '4.t1.b1', '4.w1.b1'], 'contains': ['16.d1.a1', '24.e1.b1', '56.h1.b1'], 'core': '8.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [169, 192, 336, 448, 672], 'label': '1344.8544.8.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.n1.b1', 'normal_contained_in': ['4.f1.a1', '4.k1.b1', '4.o1.b1', '4.p1.a1', '4.s1.a1', '4.t1.b1', '4.w1.b1'], 'normal_contains': ['16.d1.a1', '24.e1.b1', '56.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 74052196
    {'ambient': '1344.8544', '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': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.k1.a1', '4.o1.b1', '4.q1.b1', '4.r1.b1', '4.u1.a1', '4.v1.a1'], 'contains': ['16.d1.a1', '24.bd1.a1', '56.i1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [58, 1008, 672, 192, 448], 'label': '1344.8544.8.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.g1.a1', '4.k1.a1', '4.o1.b1', '4.q1.b1', '4.r1.b1', '4.u1.a1', '4.v1.a1'], 'normal_contains': ['16.d1.a1', '56.i1.a1'], 'normalizer': '1.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: 74052197
    {'ambient': '1344.8544', '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': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.k1.b1', '4.o1.a1', '4.q1.a1', '4.r1.a1', '4.u1.b1', '4.v1.b1'], 'contains': ['16.d1.a1', '24.bd1.b1', '56.i1.b1'], 'core': '8.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [59, 1008, 672, 192, 448], 'label': '1344.8544.8.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.o1.b1', 'normal_contained_in': ['4.g1.a1', '4.k1.b1', '4.o1.a1', '4.q1.a1', '4.r1.a1', '4.u1.b1', '4.v1.b1'], 'normal_contains': ['16.d1.a1', '56.i1.b1'], 'normalizer': '1.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: 74052198
    {'ambient': '1344.8544', '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.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.x1.a1', '4.z1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.k1.a1', '24.g1.a1', '56.j1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 448, 672, 6, 192], 'label': '1344.8544.8.p1.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.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: 74052199
    {'ambient': '1344.8544', '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': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.x1.a1', '4.z1.a1'], 'contains': ['16.a1.a1', '16.i1.a1', '16.m1.a1', '24.h1.a1', '56.k1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 672, 448, 4, 192], 'label': '1344.8544.8.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.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: 74052200
    {'ambient': '1344.8544', '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': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.y1.a1', '4.ba1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '16.j1.b1', '24.j1.a1', '56.l1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 448, 672, 750, 192], 'label': '1344.8544.8.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 74052201
    {'ambient': '1344.8544', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.y1.a1', '4.ba1.a1'], 'contains': ['16.a1.a1', '16.l1.a1', '16.l1.b1', '24.k1.a1', '56.m1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [337, 672, 448, 204, 192], 'label': '1344.8544.8.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.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}