Abstract group data - 2688.ed

Formats: - HTML - YAML - JSON - 2025-12-29T15:43:21.821802

• 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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [12, 6, 6, 12], 'aut_gens': [[63283818170, 56569774205, 56577758221, 75734235232, 50347148515, 3628800, 479001600, 3669120, 11652480], [81482209527, 75726251872, 75255232128, 50826150115, 56577757565, 479041920, 482670720, 3669120, 490654080], [57053132152, 57045187325, 75737822208, 81482254271, 44599126735, 479041920, 479001600, 3669120, 7983360], [486989462, 75247250272, 62801190843, 50826150115, 56577757565, 40320, 482670720, 3669120, 11652480], [44822, 75258862432, 63283780923, 50347148515, 57053170685, 11652480, 479001600, 3669120, 479041920]], 'aut_group': None, 'aut_hash': 8049327479272634076, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10752, 'aut_permdeg': 36, 'aut_perms': [365595036164605377484739510630509756968178, 26588530800217492934937146001059113365674, 76153302471374548713122988063034656988412, 76153302551419031957305863613556370750332], 'aut_phi_ratio': 14.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 4, 1], [2, 7, 1, 2], [2, 7, 2, 1], [2, 14, 4, 1], [3, 28, 1, 2], [4, 2, 2, 1], [4, 14, 2, 1], [6, 28, 1, 6], [6, 28, 2, 4], [6, 56, 4, 4], [7, 24, 1, 2], [12, 56, 2, 4], [14, 24, 1, 2], [14, 24, 2, 2], [14, 48, 4, 2], [28, 48, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\wr C_2^2\\times F_8:C_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '336.210', 'autcentquo_hash': 210, 'autcentquo_nilpotent': False, 'autcentquo_order': 336, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_8:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 4], [2, 7, 4], [2, 14, 4], [3, 28, 2], [4, 2, 2], [4, 14, 2], [6, 28, 14], [6, 56, 16], [7, 24, 2], [12, 56, 8], [14, 24, 6], [14, 48, 8], [28, 48, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '672.1256', 'commutator_count': 1, 'commutator_label': '112.41', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 108, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['168.43', 1], ['2.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 4], [2, 7, 1, 4], [2, 14, 1, 4], [3, 28, 2, 1], [4, 2, 1, 2], [4, 14, 1, 2], [6, 28, 2, 7], [6, 56, 2, 8], [7, 24, 2, 1], [12, 56, 2, 4], [14, 24, 2, 3], [14, 48, 2, 4], [28, 48, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 550368, 'exponent': 84, 'exponents_of_order': [7, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '1344.11688', 'hash': 7006912750036055389, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [6, 2, 14, 2, 2, 2, 1, 1, 2], 'inner_gens': [[63283818170, 44112141775, 69028209232, 75737823712, 69031798050, 40320, 479001600, 3669120, 11652480], [486987491, 56569774205, 81482250618, 75737823712, 50350736995, 3628800, 479001600, 3669120, 7983360], [486989462, 81474270911, 56577758221, 50826150115, 69028209570, 40320, 479001600, 3669120, 7983360], [63280149050, 56566185725, 44123717739, 75734235232, 50347148515, 40320, 479001600, 3669120, 7983360], [57053128848, 56566185725, 62804777727, 75734235232, 50347148515, 40320, 479001600, 3669120, 7983360], [63280149050, 56569774205, 56574169741, 75737823712, 50350736995, 3628800, 479001600, 3669120, 7983360], [63283818170, 56569774205, 56577758221, 75734235232, 50347148515, 3628800, 479001600, 3669120, 11652480], [63283818170, 56569774205, 56577758221, 75734235232, 50347148515, 3628800, 479001600, 3669120, 11652480], [63283818170, 56566185725, 56574169741, 75737823712, 50350736995, 40320, 479001600, 3669120, 11652480]], 'inner_hash': 1256, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': False, 'inner_tex': 'C_2\\times F_8:C_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 6], [3, 16], [6, 4], [7, 24], [14, 6]], 'label': '2688.ed', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'D4*F8:C6', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 80, 'number_divisions': 50, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 268, 'number_subgroup_classes': 768, 'number_subgroups': 13580, 'old_label': None, 'order': 2688, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 95], [3, 56], [4, 32], [6, 1288], [7, 48], [12, 448], [14, 528], [28, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 11612160, 0], 'outer_gens': [[63275794490, 56577797885, 56574169741, 75737823712, 50350736995, 11652480, 479001600, 3669120, 3628800], [63283818170, 57048775805, 57056759821, 75255233632, 50826150115, 482630400, 479001600, 3669120, 11652480], [62801147450, 57048775805, 56577758221, 75737823712, 50347148515, 482630400, 482670720, 3669120, 490654080], [62804816570, 57048775805, 56577758221, 75734235232, 50347148515, 482630400, 479001600, 3669120, 490654080]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [288, 7, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 2], [6, 8], [7, 8], [12, 2], [14, 10], [28, 2]], 'representations': {'PC': {'code': '2980595947887597551656875590873462464228712358117669085932761761310471188255535632703363398803384', 'gens': [1, 3, 4, 7, 8, 9], 'pres': [9, -2, -3, -2, -2, -2, -7, -2, 2, 2, 18, 77331, 32196, 1101, 102, 117724, 35113, 130, 82949, 29822, 63510, 63519, 12381, 2688, 1815, 120967, 84688, 2050, 7099, 3076, 11375, 2312, 4022]}, 'Perm': {'d': 14, 'gens': [63283818170, 56569774205, 56577758221, 75734235232, 50347148515, 3628800, 479001600, 3669120, 11652480]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_4\\times F_8:C_6', 'transitive_degree': 56, '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: 157250658
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 108, 'group_order': 2688, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 157250669
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 108, 'group_order': 2688, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 479001600, 'size': 1}
  • id: 157250680
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 108, 'group_order': 2688, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 482670720, 'size': 1}
  • id: 157250691
    {'aut_label': '2C', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 108, 'group_order': 2688, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 3669120, 'size': 1}
  • id: 157250702
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 108, 'group_order': 2688, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 40320, 'size': 2}
  • id: 157250713
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 108, 'group_order': 2688, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 7983360, 'size': 2}
  • id: 157250724
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 108, 'group_order': 2688, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 479041920, 'size': 2}
  • id: 157250735
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 108, 'group_order': 2688, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 486984960, 'size': 2}
  • id: 157250737
    {'aut_label': '2H', 'centralizer': '7.a1', 'counter': 9, 'group_counter': 108, 'group_order': 2688, 'label': '2H', 'order': 2, 'powers': [1, 9, 9], 'representative': 44112101455, 'size': 7}
  • id: 157250659
    {'aut_label': '2I', 'centralizer': '7.a1', 'counter': 10, 'group_counter': 108, 'group_order': 2688, 'label': '2I', 'order': 2, 'powers': [1, 10, 10], 'representative': 44115770575, 'size': 7}
  • id: 157250660
    {'aut_label': '2J', 'centralizer': '7.a1', 'counter': 11, 'group_counter': 108, 'group_order': 2688, 'label': '2J', 'order': 2, 'powers': [1, 11, 11], 'representative': 44591103055, 'size': 7}
  • id: 157250661
    {'aut_label': '2J', 'centralizer': '7.a1', 'counter': 12, 'group_counter': 108, 'group_order': 2688, 'label': '2K', 'order': 2, 'powers': [1, 12, 12], 'representative': 44594772175, 'size': 7}
  • id: 157250662
    {'aut_label': '2L', 'centralizer': '14.b1', 'counter': 13, 'group_counter': 108, 'group_order': 2688, 'label': '2L', 'order': 2, 'powers': [1, 13, 13], 'representative': 44599086415, 'size': 14}
  • id: 157250663
    {'aut_label': '2L', 'centralizer': '14.b1', 'counter': 14, 'group_counter': 108, 'group_order': 2688, 'label': '2M', 'order': 2, 'powers': [1, 14, 14], 'representative': 81953272511, 'size': 14}
  • id: 157250664
    {'aut_label': '2L', 'centralizer': '14.b1', 'counter': 15, 'group_counter': 108, 'group_order': 2688, 'label': '2N', 'order': 2, 'powers': [1, 15, 15], 'representative': 75250838752, 'size': 14}
  • id: 157250665
    {'aut_label': '2L', 'centralizer': '14.b1', 'counter': 16, 'group_counter': 108, 'group_order': 2688, 'label': '2O', 'order': 2, 'powers': [1, 16, 16], 'representative': 50347108195, 'size': 14}
  • id: 157250666
    {'aut_label': '3A1', 'centralizer': '28.d1', 'counter': 17, 'group_counter': 108, 'group_order': 2688, 'label': '3A1', 'order': 3, 'powers': [18, 1, 17], 'representative': 496, 'size': 28}
  • id: 157250667
    {'aut_label': '3A-1', 'centralizer': '28.d1', 'counter': 18, 'group_counter': 108, 'group_order': 2688, 'label': '3A-1', 'order': 3, 'powers': [17, 1, 18], 'representative': 212, 'size': 28}
  • id: 157250668
    {'aut_label': '4A', 'centralizer': '2.b1', 'counter': 19, 'group_counter': 108, 'group_order': 2688, 'label': '4A', 'order': 4, 'powers': [4, 19, 19], 'representative': 11612160, 'size': 2}
  • id: 157250670
    {'aut_label': '4A', 'centralizer': '2.b1', 'counter': 20, 'group_counter': 108, 'group_order': 2688, 'label': '4B', 'order': 4, 'powers': [4, 20, 20], 'representative': 490613760, 'size': 2}
  • id: 157250671
    {'aut_label': '4C', 'centralizer': '14.e1', 'counter': 21, 'group_counter': 108, 'group_order': 2688, 'label': '4C', 'order': 4, 'powers': [4, 21, 21], 'representative': 57053170685, 'size': 14}
  • id: 157250672
    {'aut_label': '4C', 'centralizer': '14.e1', 'counter': 22, 'group_counter': 108, 'group_order': 2688, 'label': '4D', 'order': 4, 'powers': [4, 22, 22], 'representative': 69031798050, 'size': 14}
  • id: 157250673
    {'aut_label': '6A1', 'centralizer': '28.d1', 'counter': 23, 'group_counter': 108, 'group_order': 2688, 'label': '6A1', 'order': 6, 'powers': [17, 2, 23], 'representative': 479001812, 'size': 28}
  • id: 157250674
    {'aut_label': '6A-1', 'centralizer': '28.d1', 'counter': 24, 'group_counter': 108, 'group_order': 2688, 'label': '6A-1', 'order': 6, 'powers': [18, 2, 24], 'representative': 479002096, 'size': 28}
  • id: 157250675
    {'aut_label': '6A1', 'centralizer': '28.d1', 'counter': 25, 'group_counter': 108, 'group_order': 2688, 'label': '6B1', 'order': 6, 'powers': [17, 3, 25], 'representative': 482670932, 'size': 28}
  • id: 157250676
    {'aut_label': '6A-1', 'centralizer': '28.d1', 'counter': 26, 'group_counter': 108, 'group_order': 2688, 'label': '6B-1', 'order': 6, 'powers': [18, 3, 26], 'representative': 482671216, 'size': 28}
  • id: 157250677
    {'aut_label': '6C1', 'centralizer': '28.d1', 'counter': 27, 'group_counter': 108, 'group_order': 2688, 'label': '6C1', 'order': 6, 'powers': [17, 9, 27], 'representative': 44112101397, 'size': 28}
  • id: 157250678
    {'aut_label': '6C-1', 'centralizer': '28.d1', 'counter': 28, 'group_counter': 108, 'group_order': 2688, 'label': '6C-1', 'order': 6, 'powers': [18, 9, 28], 'representative': 44112101717, 'size': 28}
  • id: 157250679
    {'aut_label': '6D1', 'centralizer': '28.d1', 'counter': 29, 'group_counter': 108, 'group_order': 2688, 'label': '6D1', 'order': 6, 'powers': [17, 10, 29], 'representative': 44115770517, 'size': 28}
  • id: 157250681
    {'aut_label': '6D-1', 'centralizer': '28.d1', 'counter': 30, 'group_counter': 108, 'group_order': 2688, 'label': '6D-1', 'order': 6, 'powers': [18, 10, 30], 'representative': 44115770837, 'size': 28}
  • id: 157250682
    {'aut_label': '6E1', 'centralizer': '28.d1', 'counter': 31, 'group_counter': 108, 'group_order': 2688, 'label': '6E1', 'order': 6, 'powers': [17, 11, 31], 'representative': 44591102997, 'size': 28}
  • id: 157250683
    {'aut_label': '6E-1', 'centralizer': '28.d1', 'counter': 32, 'group_counter': 108, 'group_order': 2688, 'label': '6E-1', 'order': 6, 'powers': [18, 11, 32], 'representative': 44591103317, 'size': 28}
  • id: 157250684
    {'aut_label': '6E1', 'centralizer': '28.d1', 'counter': 33, 'group_counter': 108, 'group_order': 2688, 'label': '6F1', 'order': 6, 'powers': [17, 12, 33], 'representative': 44594772117, 'size': 28}
  • id: 157250685
    {'aut_label': '6E-1', 'centralizer': '28.d1', 'counter': 34, 'group_counter': 108, 'group_order': 2688, 'label': '6F-1', 'order': 6, 'powers': [18, 12, 34], 'representative': 44594772437, 'size': 28}
  • id: 157250686
    {'aut_label': '6G1', 'centralizer': '28.d1', 'counter': 35, 'group_counter': 108, 'group_order': 2688, 'label': '6G1', 'order': 6, 'powers': [18, 4, 35], 'representative': 62796835055, 'size': 28}
  • id: 157250687
    {'aut_label': '6G-1', 'centralizer': '28.d1', 'counter': 36, 'group_counter': 108, 'group_order': 2688, 'label': '6G-1', 'order': 6, 'powers': [17, 4, 36], 'representative': 81477899548, 'size': 28}
  • id: 157250688
    {'aut_label': '6H1', 'centralizer': '56.e1', 'counter': 37, 'group_counter': 108, 'group_order': 2688, 'label': '6H1', 'order': 6, 'powers': [17, 13, 37], 'representative': 44599086357, 'size': 56}
  • id: 157250689
    {'aut_label': '6H-1', 'centralizer': '56.e1', 'counter': 38, 'group_counter': 108, 'group_order': 2688, 'label': '6H-1', 'order': 6, 'powers': [18, 13, 38], 'representative': 44599086677, 'size': 56}
  • id: 157250690
    {'aut_label': '6H1', 'centralizer': '56.e1', 'counter': 39, 'group_counter': 108, 'group_order': 2688, 'label': '6I1', 'order': 6, 'powers': [17, 14, 39], 'representative': 81953270493, 'size': 56}
  • id: 157250692
    {'aut_label': '6H-1', 'centralizer': '56.e1', 'counter': 40, 'group_counter': 108, 'group_order': 2688, 'label': '6I-1', 'order': 6, 'powers': [18, 14, 40], 'representative': 81953271999, 'size': 56}
  • id: 157250693
    {'aut_label': '6H-1', 'centralizer': '56.e1', 'counter': 41, 'group_counter': 108, 'group_order': 2688, 'label': '6J1', 'order': 6, 'powers': [18, 15, 41], 'representative': 50342755315, 'size': 56}
  • id: 157250694
    {'aut_label': '6H1', 'centralizer': '56.e1', 'counter': 42, 'group_counter': 108, 'group_order': 2688, 'label': '6J-1', 'order': 6, 'powers': [17, 15, 42], 'representative': 69023817407, 'size': 56}
  • id: 157250695
    {'aut_label': '6K1', 'centralizer': '56.e1', 'counter': 43, 'group_counter': 108, 'group_order': 2688, 'label': '6K1', 'order': 6, 'powers': [18, 7, 43], 'representative': 81953270893, 'size': 56}
  • id: 157250696
    {'aut_label': '6K-1', 'centralizer': '56.e1', 'counter': 44, 'group_counter': 108, 'group_order': 2688, 'label': '6K-1', 'order': 6, 'powers': [17, 7, 44], 'representative': 57045187785, 'size': 56}
  • id: 157250697
    {'aut_label': '6H1', 'centralizer': '56.e1', 'counter': 45, 'group_counter': 108, 'group_order': 2688, 'label': '6L1', 'order': 6, 'powers': [17, 16, 45], 'representative': 56574128082, 'size': 56}
  • id: 157250698
    {'aut_label': '6H-1', 'centralizer': '56.e1', 'counter': 46, 'group_counter': 108, 'group_order': 2688, 'label': '6L-1', 'order': 6, 'powers': [18, 16, 46], 'representative': 69028169897, 'size': 56}
  • id: 157250699
    {'aut_label': '6K-1', 'centralizer': '56.e1', 'counter': 47, 'group_counter': 108, 'group_order': 2688, 'label': '6M1', 'order': 6, 'powers': [17, 8, 47], 'representative': 57056801272, 'size': 56}
  • id: 157250700
    {'aut_label': '6K1', 'centralizer': '56.e1', 'counter': 48, 'group_counter': 108, 'group_order': 2688, 'label': '6M-1', 'order': 6, 'powers': [18, 8, 48], 'representative': 75737861177, 'size': 56}
  • id: 157250701
    {'aut_label': '6K-1', 'centralizer': '56.e1', 'counter': 49, 'group_counter': 108, 'group_order': 2688, 'label': '6N1', 'order': 6, 'powers': [17, 6, 49], 'representative': 11653490, 'size': 56}
  • id: 157250703
    {'aut_label': '6K1', 'centralizer': '56.e1', 'counter': 50, 'group_counter': 108, 'group_order': 2688, 'label': '6N-1', 'order': 6, 'powers': [18, 6, 50], 'representative': 11654712, 'size': 56}
  • id: 157250704
    {'aut_label': '6K1', 'centralizer': '56.e1', 'counter': 51, 'group_counter': 108, 'group_order': 2688, 'label': '6O1', 'order': 6, 'powers': [18, 5, 51], 'representative': 44112144051, 'size': 56}
  • id: 157250705
    {'aut_label': '6K-1', 'centralizer': '56.e1', 'counter': 52, 'group_counter': 108, 'group_order': 2688, 'label': '6O-1', 'order': 6, 'powers': [17, 5, 52], 'representative': 62793204410, 'size': 56}
  • id: 157250706
    {'aut_label': '7A1', 'centralizer': '24.c1', 'counter': 53, 'group_counter': 108, 'group_order': 2688, 'label': '7A1', 'order': 7, 'powers': [53, 54, 1], 'representative': 1765, 'size': 24}
  • id: 157250707
    {'aut_label': '7A-1', 'centralizer': '24.c1', 'counter': 54, 'group_counter': 108, 'group_order': 2688, 'label': '7A-1', 'order': 7, 'powers': [54, 53, 1], 'representative': 3482, 'size': 24}
  • id: 157250708
    {'aut_label': '12A1', 'centralizer': '56.h1', 'counter': 55, 'group_counter': 108, 'group_order': 2688, 'label': '12A1', 'order': 12, 'powers': [35, 19, 55], 'representative': 81485842588, 'size': 56}
  • id: 157250709
    {'aut_label': '12A-1', 'centralizer': '56.h1', 'counter': 56, 'group_counter': 108, 'group_order': 2688, 'label': '12A-1', 'order': 12, 'powers': [36, 19, 56], 'representative': 62801189615, 'size': 56}
  • id: 157250710
    {'aut_label': '12A-1', 'centralizer': '56.h1', 'counter': 57, 'group_counter': 108, 'group_order': 2688, 'label': '12B1', 'order': 12, 'powers': [36, 20, 57], 'representative': 487026402, 'size': 56}
  • id: 157250711
    {'aut_label': '12A1', 'centralizer': '56.h1', 'counter': 58, 'group_counter': 108, 'group_order': 2688, 'label': '12B-1', 'order': 12, 'powers': [35, 20, 58], 'representative': 490616677, 'size': 56}
  • id: 157250712
    {'aut_label': '12C1', 'centralizer': '56.h1', 'counter': 59, 'group_counter': 108, 'group_order': 2688, 'label': '12C1', 'order': 12, 'powers': [35, 21, 59], 'representative': 63283781915, 'size': 56}
  • id: 157250714
    {'aut_label': '12C-1', 'centralizer': '56.h1', 'counter': 60, 'group_counter': 108, 'group_order': 2688, 'label': '12C-1', 'order': 12, 'powers': [36, 21, 60], 'representative': 81961253693, 'size': 56}
  • id: 157250715
    {'aut_label': '12C-1', 'centralizer': '56.h1', 'counter': 61, 'group_counter': 108, 'group_order': 2688, 'label': '12D1', 'order': 12, 'powers': [36, 22, 61], 'representative': 44120128579, 'size': 56}
  • id: 157250716
    {'aut_label': '12C1', 'centralizer': '56.h1', 'counter': 62, 'group_counter': 108, 'group_order': 2688, 'label': '12D-1', 'order': 12, 'powers': [35, 22, 62], 'representative': 56577755206, 'size': 56}
  • id: 157250717
    {'aut_label': '14A1', 'centralizer': '24.c1', 'counter': 63, 'group_counter': 108, 'group_order': 2688, 'label': '14A1', 'order': 14, 'powers': [53, 64, 2], 'representative': 479002481, 'size': 24}
  • id: 157250718
    {'aut_label': '14A-1', 'centralizer': '24.c1', 'counter': 64, 'group_counter': 108, 'group_order': 2688, 'label': '14A-1', 'order': 14, 'powers': [54, 63, 2], 'representative': 479004332, 'size': 24}
  • id: 157250719
    {'aut_label': '14A1', 'centralizer': '24.c1', 'counter': 65, 'group_counter': 108, 'group_order': 2688, 'label': '14B1', 'order': 14, 'powers': [53, 66, 3], 'representative': 482671601, 'size': 24}
  • id: 157250720
    {'aut_label': '14A-1', 'centralizer': '24.c1', 'counter': 66, 'group_counter': 108, 'group_order': 2688, 'label': '14B-1', 'order': 14, 'powers': [54, 65, 3], 'representative': 482673452, 'size': 24}
  • id: 157250721
    {'aut_label': '14C1', 'centralizer': '24.c1', 'counter': 67, 'group_counter': 108, 'group_order': 2688, 'label': '14C1', 'order': 14, 'powers': [53, 68, 4], 'representative': 3670885, 'size': 24}
  • id: 157250722
    {'aut_label': '14C-1', 'centralizer': '24.c1', 'counter': 68, 'group_counter': 108, 'group_order': 2688, 'label': '14C-1', 'order': 14, 'powers': [54, 67, 4], 'representative': 3672602, 'size': 24}
  • id: 157250723
    {'aut_label': '14D1', 'centralizer': '48.b1', 'counter': 69, 'group_counter': 108, 'group_order': 2688, 'label': '14D1', 'order': 14, 'powers': [53, 70, 5], 'representative': 41201, 'size': 48}
  • id: 157250725
    {'aut_label': '14D-1', 'centralizer': '48.b1', 'counter': 70, 'group_counter': 108, 'group_order': 2688, 'label': '14D-1', 'order': 14, 'powers': [54, 69, 5], 'representative': 43052, 'size': 48}
  • id: 157250726
    {'aut_label': '14D1', 'centralizer': '48.b1', 'counter': 71, 'group_counter': 108, 'group_order': 2688, 'label': '14E1', 'order': 14, 'powers': [53, 72, 6], 'representative': 7984241, 'size': 48}
  • id: 157250727
    {'aut_label': '14D-1', 'centralizer': '48.b1', 'counter': 72, 'group_counter': 108, 'group_order': 2688, 'label': '14E-1', 'order': 14, 'powers': [54, 71, 6], 'representative': 7986092, 'size': 48}
  • id: 157250728
    {'aut_label': '14D1', 'centralizer': '48.b1', 'counter': 73, 'group_counter': 108, 'group_order': 2688, 'label': '14F1', 'order': 14, 'powers': [53, 74, 7], 'representative': 479042801, 'size': 48}
  • id: 157250729
    {'aut_label': '14D-1', 'centralizer': '48.b1', 'counter': 74, 'group_counter': 108, 'group_order': 2688, 'label': '14F-1', 'order': 14, 'powers': [54, 73, 7], 'representative': 479044652, 'size': 48}
  • id: 157250730
    {'aut_label': '14D1', 'centralizer': '48.b1', 'counter': 75, 'group_counter': 108, 'group_order': 2688, 'label': '14G1', 'order': 14, 'powers': [53, 76, 8], 'representative': 486985841, 'size': 48}
  • id: 157250731
    {'aut_label': '14D-1', 'centralizer': '48.b1', 'counter': 76, 'group_counter': 108, 'group_order': 2688, 'label': '14G-1', 'order': 14, 'powers': [54, 75, 8], 'representative': 486987692, 'size': 48}
  • id: 157250732
    {'aut_label': '28A1', 'centralizer': '48.c1', 'counter': 77, 'group_counter': 108, 'group_order': 2688, 'label': '28A1', 'order': 28, 'powers': [67, 78, 19], 'representative': 8024561, 'size': 48}
  • id: 157250733
    {'aut_label': '28A-1', 'centralizer': '48.c1', 'counter': 78, 'group_counter': 108, 'group_order': 2688, 'label': '28A-1', 'order': 28, 'powers': [68, 77, 19], 'representative': 8026412, 'size': 48}
  • id: 157250734
    {'aut_label': '28A1', 'centralizer': '48.c1', 'counter': 79, 'group_counter': 108, 'group_order': 2688, 'label': '28B1', 'order': 28, 'powers': [67, 80, 20], 'representative': 487026161, 'size': 48}
  • id: 157250736
    {'aut_label': '28A-1', 'centralizer': '48.c1', 'counter': 80, 'group_counter': 108, 'group_order': 2688, 'label': '28B-1', 'order': 28, 'powers': [68, 79, 20], 'representative': 487028012, 'size': 48}
• 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: 15356435
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.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], 'schur_index': 1}
  • id: 15356446
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.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], 'schur_index': 1}
  • id: 15356457
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.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], 'schur_index': 1}
  • id: 15356468
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.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], 'schur_index': 1}
  • id: 15356479
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.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], 'schur_index': 1}
  • id: 15356481
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.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], 'schur_index': 1}
  • id: 15356482
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.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], 'schur_index': 1}
  • id: 15356483
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.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], 'schur_index': 1}
  • id: 15356484
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 15356436
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, -1, -1, -2, 2, 2, -2, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 2, 2, -1, -1, 1, 1, -1, -1, 1, 1, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 15356437
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -1, -1, 2, -2, -2, 2, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 2, 2, 1, 1, -1, -1, 1, 1, -1, -1, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 15356438
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -1, -1, 2, -2, -2, 2, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 2, 2, 1, 1, -1, -1, 1, 1, -1, -1, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 15356439
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, -1, -1, -2, 2, 2, -2, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 2, 2, -1, -1, 1, 1, -1, -1, 1, 1, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 15356440
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 15356441
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -1, -1, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 15356442
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, 2, 2, -2, -1, -1, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 15356443
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 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, 2, 2, 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], 'schur_index': 1}
  • id: 15356444
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 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, 2, 2, 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], 'schur_index': 1}
  • id: 15356445
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.2c', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, -4, 4, 4, -4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -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, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356447
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.2d', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, -4, 4, -4, 4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -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, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356448
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.3a', 'multiplicity': 2, 'nt': [7, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 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], 'schur_index': 1}
  • id: 15356449
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.3b', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -6, -6, 6, 6, 6, 6, -6, -6, 6, -6, 6, -6, 0, 0, -6, 6, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 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], 'schur_index': 1}
  • id: 15356450
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.3c', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -6, 6, -6, 6, 6, 6, -6, -6, -6, -6, 6, 6, 0, 0, 6, -6, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 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], 'schur_index': 1}
  • id: 15356451
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.3d', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, -6, 6, -6, 6, 6, -6, -6, 6, 6, -6, -6, 0, 0, 6, -6, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 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], 'schur_index': 1}
  • id: 15356452
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.3e', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 6, 6, -6, -6, 6, 6, -6, -6, -6, 6, -6, 6, 0, 0, -6, 6, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 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], 'schur_index': 1}
  • id: 15356453
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.3f', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, -6, -6, -6, 6, 6, 6, 6, -6, -6, -6, -6, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 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], 'schur_index': 1}
  • id: 15356454
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.3g', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -6, 6, 6, -6, 6, 6, 6, 6, 6, -6, -6, 6, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 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], 'schur_index': 1}
  • id: 15356455
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.3h', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, -6, -6, 6, 6, 6, 6, 6, -6, 6, 6, -6, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 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], 'schur_index': 1}
  • id: 15356459
    {'cdim': 7, 'counter': 31, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7a', 'multiplicity': 1, 'nt': [8, 36], 'qdim': 7, 'qvalues': [7, 7, 7, 7, 7, 7, 7, 7, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 7, 7, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356460
    {'cdim': 7, 'counter': 32, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7b', 'multiplicity': 1, 'nt': [14, 18], 'qdim': 7, 'qvalues': [7, -7, -7, 7, -7, -7, 7, 7, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -7, 7, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356461
    {'cdim': 7, 'counter': 33, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7c', 'multiplicity': 1, 'nt': [14, 18], 'qdim': 7, 'qvalues': [7, -7, -7, 7, -7, 7, -7, 7, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 7, -7, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356462
    {'cdim': 7, 'counter': 34, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7d', 'multiplicity': 1, 'nt': [14, 18], 'qdim': 7, 'qvalues': [7, -7, -7, 7, 7, -7, 7, -7, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 7, -7, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356463
    {'cdim': 7, 'counter': 35, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7e', 'multiplicity': 1, 'nt': [14, 18], 'qdim': 7, 'qvalues': [7, -7, -7, 7, 7, 7, -7, -7, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -7, 7, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356464
    {'cdim': 7, 'counter': 36, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7f', 'multiplicity': 1, 'nt': [14, 18], 'qdim': 7, 'qvalues': [7, 7, 7, 7, -7, -7, -7, -7, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 7, 7, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356465
    {'cdim': 7, 'counter': 37, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7g', 'multiplicity': 1, 'nt': [14, 18], 'qdim': 7, 'qvalues': [7, 7, 7, 7, -7, 7, 7, -7, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -7, -7, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356466
    {'cdim': 7, 'counter': 38, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7h', 'multiplicity': 1, 'nt': [14, 18], 'qdim': 7, 'qvalues': [7, 7, 7, 7, 7, -7, -7, 7, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -7, -7, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356456
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.6a', 'multiplicity': 2, 'nt': [28, 22], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 0, 0, 0, 0, -12, 12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 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], 'schur_index': 1}
  • id: 15356458
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.6b', 'multiplicity': 2, 'nt': [28, 22], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 0, 0, 0, 0, -12, 12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 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], 'schur_index': 1}
  • id: 15356467
    {'cdim': 7, 'counter': 39, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7i', 'multiplicity': 2, 'nt': [24, 283], 'qdim': 14, 'qvalues': [14, 14, 14, 14, 14, 14, 14, 14, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, 14, 14, -2, -2, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356469
    {'cdim': 7, 'counter': 40, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7j', 'multiplicity': 2, 'nt': [42, 67], 'qdim': 14, 'qvalues': [14, -14, -14, 14, -14, -14, 14, 14, -2, -2, 2, 2, -2, 2, -2, 2, -1, -1, -14, 14, -2, 2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356470
    {'cdim': 7, 'counter': 41, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7k', 'multiplicity': 2, 'nt': [42, 67], 'qdim': 14, 'qvalues': [14, -14, -14, 14, -14, 14, -14, 14, -2, -2, 2, 2, 2, 2, -2, -2, -1, -1, 14, -14, 2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356471
    {'cdim': 7, 'counter': 42, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7l', 'multiplicity': 2, 'nt': [42, 67], 'qdim': 14, 'qvalues': [14, -14, -14, 14, 14, -14, 14, -14, -2, -2, 2, 2, -2, -2, 2, 2, -1, -1, 14, -14, 2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356472
    {'cdim': 7, 'counter': 43, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7m', 'multiplicity': 2, 'nt': [42, 67], 'qdim': 14, 'qvalues': [14, -14, -14, 14, 14, 14, -14, -14, -2, -2, 2, 2, 2, -2, 2, -2, -1, -1, -14, 14, -2, 2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356473
    {'cdim': 7, 'counter': 44, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7n', 'multiplicity': 2, 'nt': [42, 67], 'qdim': 14, 'qvalues': [14, 14, 14, 14, -14, -14, -14, -14, -2, -2, -2, -2, 2, 2, 2, 2, -1, -1, 14, 14, -2, -2, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356474
    {'cdim': 7, 'counter': 45, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7o', 'multiplicity': 2, 'nt': [42, 67], 'qdim': 14, 'qvalues': [14, 14, 14, 14, -14, 14, 14, -14, -2, -2, -2, -2, -2, 2, 2, -2, -1, -1, -14, -14, 2, 2, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356475
    {'cdim': 7, 'counter': 46, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.7p', 'multiplicity': 2, 'nt': [42, 67], 'qdim': 14, 'qvalues': [14, 14, 14, 14, 14, -14, -14, 14, -2, -2, -2, -2, 2, -2, -2, 2, -1, -1, -14, -14, 2, 2, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356476
    {'cdim': 14, 'counter': 47, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.14a', 'multiplicity': 1, 'nt': [28, 145], 'qdim': 14, 'qvalues': [14, -14, 14, -14, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356477
    {'cdim': 14, 'counter': 48, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.14b', 'multiplicity': 1, 'nt': [28, 145], 'qdim': 14, 'qvalues': [14, 14, -14, -14, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356478
    {'cdim': 14, 'counter': 49, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.14c', 'multiplicity': 2, 'nt': [84, 0], 'qdim': 28, 'qvalues': [28, -28, 28, -28, 0, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15356480
    {'cdim': 14, 'counter': 50, 'faithful': False, 'group': '2688.ed', 'group_order': 2688, 'image': None, 'label': '2688.ed.14d', 'multiplicity': 2, 'nt': [84, 0], 'qdim': 28, 'qvalues': [28, 28, -28, -28, 0, 0, 0, 0, 4, -4, 4, -4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 35190700
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 2688, 'label': '2688.ed.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]]]}
  • id: 35190711
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 1344, 'label': '2688.ed.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]]]}
  • id: 35190722
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 1344, 'label': '2688.ed.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190733
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 1344, 'label': '2688.ed.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190744
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 1344, 'label': '2688.ed.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190755
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 1344, 'label': '2688.ed.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190766
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 1344, 'label': '2688.ed.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190777
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 1344, 'label': '2688.ed.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190779
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 896, 'label': '2688.ed.1i1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190701
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 896, 'label': '2688.ed.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190702
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 448, 'label': '2688.ed.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190703
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 448, 'label': '2688.ed.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190704
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 448, 'label': '2688.ed.1k1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190705
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 448, 'label': '2688.ed.1k2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190706
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 448, 'label': '2688.ed.1l1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190707
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 448, 'label': '2688.ed.1l2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190708
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 448, 'label': '2688.ed.1m1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190709
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1', 'kernel_order': 448, 'label': '2688.ed.1m2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190710
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 448, 'label': '2688.ed.1n1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190712
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 448, 'label': '2688.ed.1n2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35190713
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 448, 'label': '2688.ed.1o1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190714
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 448, 'label': '2688.ed.1o2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190715
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 448, 'label': '2688.ed.1p1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190716
    {'center': '1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 448, 'label': '2688.ed.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35190717
    {'center': '4.a1', 'center_index': 4, 'center_order': 672, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 336, 'label': '2688.ed.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-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]], [[2, 0]], [[2, 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]]]}
  • id: 35190718
    {'center': '4.a1', 'center_index': 4, 'center_order': 672, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 336, 'label': '2688.ed.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-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]], [[2, 0]], [[2, 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]]]}
  • id: 35190719
    {'center': '4.a1', 'center_index': 4, 'center_order': 672, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 112, 'label': '2688.ed.2c1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-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]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-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: 35190720
    {'center': '4.a1', 'center_index': 4, 'center_order': 672, 'counter': 28, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 112, 'label': '2688.ed.2c2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-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]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-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: 35190721
    {'center': '4.a1', 'center_index': 4, 'center_order': 672, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 112, 'label': '2688.ed.2d1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, -1]], [[2, 1]], [[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]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-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: 35190723
    {'center': '4.a1', 'center_index': 4, 'center_order': 672, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 112, 'label': '2688.ed.2d2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, 1]], [[2, -1]], [[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]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-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: 35190724
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 31, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '21.1', 'image_order': 21, 'indicator': 0, 'kernel': '21.a1', 'kernel_order': 128, 'label': '2688.ed.3a1', 'nt': [7, 3], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]]]}
  • id: 35190725
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 32, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '21.1', 'image_order': 21, 'indicator': 0, 'kernel': '21.a1', 'kernel_order': 128, 'label': '2688.ed.3a2', 'nt': [7, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35190726
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 33, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1', 'kernel_order': 64, 'label': '2688.ed.3b1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]]]}
  • id: 35190727
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 34, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1', 'kernel_order': 64, 'label': '2688.ed.3b2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35190728
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 35, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1', 'kernel_order': 64, 'label': '2688.ed.3c1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35190729
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 36, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1', 'kernel_order': 64, 'label': '2688.ed.3c2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]]]}
  • id: 35190730
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 37, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1', 'kernel_order': 64, 'label': '2688.ed.3d1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35190731
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 38, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1', 'kernel_order': 64, 'label': '2688.ed.3d2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]]]}
  • id: 35190732
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 39, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1', 'kernel_order': 64, 'label': '2688.ed.3e1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]]]}
  • id: 35190734
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 40, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.c1', 'kernel_order': 64, 'label': '2688.ed.3e2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35190735
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 41, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.b1', 'kernel_order': 64, 'label': '2688.ed.3f1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]]]}
  • id: 35190736
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 42, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.b1', 'kernel_order': 64, 'label': '2688.ed.3f2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35190737
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 43, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1', 'kernel_order': 64, 'label': '2688.ed.3g1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35190738
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 44, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1', 'kernel_order': 64, 'label': '2688.ed.3g2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]]]}
  • id: 35190739
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 45, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1', 'kernel_order': 64, 'label': '2688.ed.3h1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35190740
    {'center': '21.a1', 'center_index': 21, 'center_order': 128, 'counter': 46, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1', 'kernel_order': 64, 'label': '2688.ed.3h2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]]]}
  • id: 35190741
    {'center': '84.a1', 'center_index': 84, 'center_order': 32, 'counter': 47, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.a1', 'kernel_order': 16, 'label': '2688.ed.6a1', 'nt': [28, 22], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190742
    {'center': '84.a1', 'center_index': 84, 'center_order': 32, 'counter': 48, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.a1', 'kernel_order': 16, 'label': '2688.ed.6a2', 'nt': [28, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190743
    {'center': '84.a1', 'center_index': 84, 'center_order': 32, 'counter': 49, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.a1', 'kernel_order': 16, 'label': '2688.ed.6b1', 'nt': [28, 22], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190745
    {'center': '84.a1', 'center_index': 84, 'center_order': 32, 'counter': 50, 'cyclotomic_n': 7, 'dim': 6, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '168.20', 'image_order': 168, 'indicator': 0, 'kernel': '168.a1', 'kernel_order': 16, 'label': '2688.ed.6b2', 'nt': [28, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[-2, 1], [-2, 2], [-2, -3]], [[2, 0], [2, 1], [2, 2], [2, -3]], [[-2, 0], [-2, 1], [-2, 2], [-2, -3]], [[2, 1], [2, 2], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190746
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 51, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '168.43', 'image_order': 168, 'indicator': 1, 'kernel': '168.b1', 'kernel_order': 16, 'label': '2688.ed.7a', 'nt': [8, 36], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190747
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 52, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7b', 'nt': [14, 18], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190748
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 53, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7c', 'nt': [14, 18], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190749
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 54, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7d', 'nt': [14, 18], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190750
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 55, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 1, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7e', 'nt': [14, 18], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190751
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 56, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 1, 'kernel': '336.b1', 'kernel_order': 8, 'label': '2688.ed.7f', 'nt': [14, 18], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190752
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 57, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 8, 'label': '2688.ed.7g', 'nt': [14, 18], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190753
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 58, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1', 'kernel_order': 8, 'label': '2688.ed.7h', 'nt': [14, 18], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190754
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 59, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '168.43', 'image_order': 168, 'indicator': 0, 'kernel': '168.b1', 'kernel_order': 16, 'label': '2688.ed.7i1', 'nt': [24, 283], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190756
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 60, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '168.43', 'image_order': 168, 'indicator': 0, 'kernel': '168.b1', 'kernel_order': 16, 'label': '2688.ed.7i2', 'nt': [24, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190757
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 61, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7j1', 'nt': [42, 67], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190758
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 62, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7j2', 'nt': [42, 2], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190759
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 63, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7k1', 'nt': [42, 67], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190760
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 64, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7k2', 'nt': [42, 2], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190761
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 65, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7l1', 'nt': [42, 67], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190762
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 66, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7l2', 'nt': [42, 2], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190763
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 67, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7m1', 'nt': [42, 67], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190764
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 68, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.c1', 'kernel_order': 8, 'label': '2688.ed.7m2', 'nt': [42, 2], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190765
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 69, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.b1', 'kernel_order': 8, 'label': '2688.ed.7n1', 'nt': [42, 67], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190767
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 70, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.b1', 'kernel_order': 8, 'label': '2688.ed.7n2', 'nt': [42, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190768
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 71, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1', 'kernel_order': 8, 'label': '2688.ed.7o1', 'nt': [42, 67], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190769
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 72, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1', 'kernel_order': 8, 'label': '2688.ed.7o2', 'nt': [42, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190770
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 73, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1', 'kernel_order': 8, 'label': '2688.ed.7p1', 'nt': [42, 67], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190771
    {'center': '168.b1', 'center_index': 168, 'center_order': 16, 'counter': 74, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1', 'kernel_order': 8, 'label': '2688.ed.7p2', 'nt': [42, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35190772
    {'center': '672.a1', 'center_index': 672, 'center_order': 4, 'counter': 75, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11307', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.a1', 'kernel_order': 2, 'label': '2688.ed.14a', 'nt': [28, 145], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190773
    {'center': '672.a1', 'center_index': 672, 'center_order': 4, 'counter': 76, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11307', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.a1', 'kernel_order': 2, 'label': '2688.ed.14b', 'nt': [28, 145], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[-14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190774
    {'center': '672.a1', 'center_index': 672, 'center_order': 4, 'counter': 77, 'cyclotomic_n': 3, 'dim': 14, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11307', 'image_order': 1344, 'indicator': 0, 'kernel': '1344.a1', 'kernel_order': 2, 'label': '2688.ed.14c1', 'nt': [84, 0], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190775
    {'center': '672.a1', 'center_index': 672, 'center_order': 4, 'counter': 78, 'cyclotomic_n': 3, 'dim': 14, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11307', 'image_order': 1344, 'indicator': 0, 'kernel': '1344.a1', 'kernel_order': 2, 'label': '2688.ed.14c2', 'nt': [84, 2], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190776
    {'center': '672.a1', 'center_index': 672, 'center_order': 4, 'counter': 79, 'cyclotomic_n': 3, 'dim': 14, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11307', 'image_order': 1344, 'indicator': 0, 'kernel': '1344.a1', 'kernel_order': 2, 'label': '2688.ed.14d1', 'nt': [84, 0], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[-14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 35190778
    {'center': '672.a1', 'center_index': 672, 'center_order': 4, 'counter': 80, 'cyclotomic_n': 3, 'dim': 14, 'faithful': False, 'field': [1, -1, 1], 'group': '2688.ed', 'group_counter': 108, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11307', 'image_order': 1344, 'indicator': 0, 'kernel': '1344.a1', 'kernel_order': 2, 'label': '2688.ed.14d2', 'nt': [84, 2], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[-14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 182282400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 2688, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '2688.ed.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2688.ed', 'subgroup_hash': 7006912750036055389, 'subgroup_order': 2688, 'subgroup_tex': 'D_4\\times F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1344, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11688', 'subgroup_hash': 11688, 'subgroup_order': 1344, 'subgroup_tex': 'C_2^2\\times F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 1344, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11306', 'subgroup_hash': 11306, 'subgroup_order': 1344, 'subgroup_tex': 'C_2\\times F_8:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 182282602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1344, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2688.ed.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11307', 'subgroup_hash': 11307, 'subgroup_order': 1344, 'subgroup_tex': 'D_4\\times F_8:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 182282613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 896, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 14, 'label': '2688.ed.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '896.19306', 'subgroup_hash': 19306, 'subgroup_order': 896, 'subgroup_tex': 'C_2^6:C_{14}', 'supersolvable': False, 'sylow': 0}
  • id: 182282624
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': True, 'core_order': 672, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '672.1256', 'subgroup_hash': 1256, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 672, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1256', 'subgroup_hash': 1256, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 672, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1049', 'subgroup_hash': 1049, 'subgroup_order': 672, 'subgroup_tex': 'F_8:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 182282657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 336, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '672.1256', 'subgroup_hash': 1256, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 448, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '448.1392', 'subgroup_hash': 1392, 'subgroup_order': 448, 'subgroup_tex': 'C_2^3\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 448, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '448.1362', 'subgroup_hash': 1362, 'subgroup_order': 448, 'subgroup_tex': 'C_2^4:C_{28}', 'supersolvable': False, 'sylow': 0}
  • id: 182282423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 448, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '448.1363', 'subgroup_hash': 1363, 'subgroup_order': 448, 'subgroup_tex': 'D_4\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '2688.ed.7.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '384.20102', 'subgroup_hash': 20102, 'subgroup_order': 384, 'subgroup_tex': 'C_2^6:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': False, 'core_order': 336, 'counter': 14, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2688.ed.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.210', 'subgroup_hash': 210, 'subgroup_order': 336, 'subgroup_tex': 'F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': True, 'core_order': 336, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.210', 'subgroup_hash': 210, 'subgroup_order': 336, 'subgroup_tex': 'F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.8.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '336.165', 'subgroup_hash': 165, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282478
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '336.210', 'subgroup_hash': 210, 'subgroup_order': 336, 'subgroup_tex': 'F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282489
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 224, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '224.195', 'subgroup_hash': 195, 'subgroup_order': 224, 'subgroup_tex': 'C_2^2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282500
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 224, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.195', 'subgroup_hash': 195, 'subgroup_order': 224, 'subgroup_tex': 'C_2^2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282512
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 224, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.173', 'subgroup_hash': 173, 'subgroup_order': 224, 'subgroup_tex': 'C_4\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '224.195', 'subgroup_hash': 195, 'subgroup_order': 224, 'subgroup_tex': 'C_2^2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.14.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.14.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1539', 'subgroup_hash': 1539, 'subgroup_order': 192, 'subgroup_tex': 'A_4\\times C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 182282556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.14.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.14.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.14.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1496', 'subgroup_hash': 1496, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 182282588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.14.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.14.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182282590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': True, 'core_order': 168, 'counter': 29, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2688.ed.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.43', 'subgroup_hash': 43, 'subgroup_order': 168, 'subgroup_tex': 'F_8:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 182282592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.51', 'subgroup_hash': 51, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.19', 'subgroup_hash': 19, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '168.20', 'subgroup_hash': 20, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 128, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 2, 'label': '2688.ed.21.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '21.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '21.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 21, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2320', 'subgroup_hash': 2320, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times C_2^4', 'supersolvable': True, 'sylow': 2}
  • id: 182282596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 112, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 112, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 16, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.38', 'subgroup_hash': 38, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 182282599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282605
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 182282607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 182282608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 182282615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.28.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 182282617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282620
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '84.2', 'subgroup_hash': 2, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 64, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.42.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '42.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 182282622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.42.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '42.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.260', 'subgroup_hash': 260, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 64, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.42.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '42.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.42.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.42.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.42.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.42.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 56, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.45', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.11', 'subgroup_hash': 11, 'subgroup_order': 56, 'subgroup_tex': 'F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182282630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 182282631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 182282632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 8, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.56.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282656
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282658
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282659
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.84.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '84.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}:C_6', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 182282661
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 32, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.84.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '84.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 182282662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 32, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.84.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '84.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282663
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 182282664
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 182282665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 182282667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 16, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 182282405
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282406
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282408
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 182282409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.84.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 182282417
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 182282418
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.96.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 182282419
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.96.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 182282420
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282421
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282424
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282425
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282429
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282433
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282438
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282439
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282440
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282441
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.112.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282443
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 21, 'label': '2688.ed.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 182282444
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.168.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.20', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{28}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 672, 'characteristic': True, 'core_order': 16, 'counter': 140, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2688.ed.168.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.43', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_8:C_3', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, '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: 182282447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 141, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.168.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{14}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282448
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282449
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282450
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282451
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282452
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 8, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 8, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282459
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282464
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282482
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.168.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182282485
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.192.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 182282486
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 177, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.192.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 182282487
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.192.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 182282488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282498
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 188, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.224.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282499
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.224.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 182282501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182282504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.224.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182282505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': False, 'core_order': 8, 'counter': 194, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.336.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.210', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 210, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_8:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282506
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 8, 'counter': 195, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.336.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.210', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 210, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_8:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 182282507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 672, 'characteristic': False, 'core_order': 8, 'counter': 196, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2688.ed.336.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.210', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 210, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_8:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 197, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.336.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.165', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 165, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{28}:C_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282509
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282513
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282516
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282517
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 4, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282518
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282519
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282520
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282521
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282524
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282527
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282529
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282535
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282537
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282538
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282540
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282541
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282543
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.336.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182282547
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '2688.ed.384.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 182282548
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.448.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 448, 'quotient_simple': 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: 182282549
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.448.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 448, 'quotient_simple': 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: 182282550
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.448.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 448, 'quotient_simple': 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: 182282551
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.448.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 448, 'quotient_simple': 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: 182282552
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.448.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 448, 'quotient_simple': 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: 182282553
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.448.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 448, 'quotient_simple': 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: 182282554
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.448.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 448, 'quotient_simple': 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: 182282555
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 2688, 'characteristic': True, 'core_order': 4, 'counter': 239, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.672.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '672.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '672.1256', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1256, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times F_8:C_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1'], '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: 182282557
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': False, 'core_order': 4, 'counter': 240, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ed.672.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '672.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '672.1256', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1256, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times F_8:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182282558
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2688.ed.672.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '672.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '672.1256', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1256, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times F_8:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182282559
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': False, 'core_order': 2, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282562
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282564
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282566
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.672.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282575
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282576
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282577
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ed.672.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': 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: 182282579
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '2688.ed.896.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '896.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 896, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 182282580
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 2688, 'characteristic': False, 'core_order': 2, 'counter': 261, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '2688.ed.1344.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1344.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1344.11307', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11307, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_4\\times F_8:C_3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 182282581
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 2688, 'characteristic': True, 'core_order': 2, 'counter': 262, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2688.ed.1344.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1344.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1344.11688', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11688, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times F_8:C_6', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], '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: 182282582
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.1344.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1344.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1344, '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: 182282583
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.1344.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1344.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1344, '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: 182282584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.1344.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1344.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1344, '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: 182282585
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.1344.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1344.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1344, '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: 182282586
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ed.1344.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1344.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1344, '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: 182282587
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ed', 'ambient_counter': 108, 'ambient_order': 2688, 'ambient_tex': 'D_4\\times F_8:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 2688, 'characteristic': True, 'core_order': 1, 'counter': 268, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '2688.ed.2688.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2688.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '2688.ed', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7006912750036055389, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 2688, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_4\\times F_8:C_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 182282472
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '168.z1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.i1', '84.q1', '84.r1', '84.s1', '84.u1'], 'contains': ['336.r1', '336.s1', '336.y1', '336.z1'], 'core': '672.c1', 'coset_action_label': None, 'count': 84, 'diagramx': [9554, -1, 9180, -1], 'generators': [56566145405, 56577757565, 3669120, 81485883071], 'label': '2688.ed.168.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.z1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282408
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '84.o1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '12.5', 'aut_weyl_index': 896, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.i1', '42.a1', '42.g1'], 'contains': ['168.q1', '168.s1', '168.w1', '168.bb1', '168.bc1', '168.bh1', '168.bj1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [5273, -1, 4254, -1], 'generators': [57045187325, 56566145405, 3669120, 69499187490, 81474230591], 'label': '2688.ed.84.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.o1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.o1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282409
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '84.p1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.5', 'aut_weyl_index': 896, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['28.j1', '42.c1', '42.d1', '42.g1'], 'contains': ['168.r1', '168.s1', '168.ba1', '168.bc1', '168.be1'], 'core': '672.b1', 'coset_action_label': None, 'count': 56, 'diagramx': [7569, -1, 7306, -1], 'generators': [56566145405, 75258822112, 3669120, 11652480, 81474230591], 'label': '2688.ed.84.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.p1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.p1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282410
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '84.q1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.11', 'aut_weyl_index': 672, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['42.e1', '42.g1'], 'contains': ['168.q1', '168.r1', '168.t1', '168.u1', '168.v1', '168.x1', '168.z1', '168.bf1'], 'core': '336.c1', 'coset_action_label': None, 'count': 84, 'diagramx': [8551, -1, 8830, -1], 'generators': [56566145405, 50350736995, 490654080, 3669120, 81485883071], 'label': '2688.ed.84.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.q1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282530
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '336.w1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['112.o1', '168.l1', '168.v1', '168.x1', '168.bf1'], 'contains': ['672.c1', '672.i1', '672.k1'], 'core': '672.c1', 'coset_action_label': None, 'count': 14, 'diagramx': [9822, -1, 8083, -1], 'generators': [57045147005, 11612160, 3669120], 'label': '2688.ed.336.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.w1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282411
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '84.r1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.l1', '42.c1', '42.e1', '42.g1'], 'contains': ['168.r1', '168.s1', '168.u1', '168.z1', '168.bd1'], 'core': '336.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [8081, -1, 7983, -1], 'generators': [56566145405, 56577757565, 3669120, 11652480, 81474230591], 'label': '2688.ed.84.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.r1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.r1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282431
    {'ambient': '2688.ed', 'aut_centralizer_order': 12, 'aut_label': '112.k1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['28.j1', '56.f1', '56.l1', '56.m1'], 'contains': ['224.f1', '224.i1', '224.k1', '336.p1'], 'core': '672.b1', 'coset_action_label': None, 'count': 224, 'diagramx': [5935, -1, 5865, -1], 'generators': [1122, 56577757565, 3669120, 11652480], 'label': '2688.ed.112.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.k1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282432
    {'ambient': '2688.ed', 'aut_centralizer_order': 12, 'aut_label': '112.l1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '28.l1', '56.g1', '56.l1', '56.m1'], 'contains': ['224.f1', '224.j1', '336.c1'], 'core': '336.c1', 'coset_action_label': None, 'count': 112, 'diagramx': [6262, -1, 6536, -1], 'generators': [1122, 11612160, 3669120, 11652480], 'label': '2688.ed.112.l1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.l1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282433
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '112.m1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.o1', '56.h1', '56.l1'], 'contains': ['224.g1', '224.j1', '224.k1', '336.s1'], 'core': '672.c1', 'coset_action_label': None, 'count': 56, 'diagramx': [6438, -1, 6201, -1], 'generators': [1122, 56566145405, 56577757565, 3669120], 'label': '2688.ed.112.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.m1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282531
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '336.x1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['168.m1', '168.t1', '168.x1', '168.y1', '168.bg1'], 'contains': ['672.i1', '672.k1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 42, 'diagramx': [9001, -1, 8876, -1], 'generators': [57045147005, 75258822112, 3669120], 'label': '2688.ed.336.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.x1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282434
    {'ambient': '2688.ed', 'aut_centralizer_order': 2, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '768.1084716', 'aut_weyl_index': 14, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['14.a1', '14.b1', '14.c1', '14.d1', '14.e1', '14.f1', '14.g1', '21.a1', '28.d1'], 'core': '21.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5913, -1, 6180, -1], 'generators': [63283818170, 69020185890, 56566145405, 44112103731, 56577757565, 3669120, 11652480, 81474230591], 'label': '2688.ed.7.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '7.a1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282407
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '84.n1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1344, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['42.d1', '42.g1'], 'contains': ['168.q1', '168.r1', '168.t1', '168.w1', '168.y1', '168.ba1', '168.bg1'], 'core': '672.b1', 'coset_action_label': None, 'count': 168, 'diagramx': [8375, -1, 8660, -1], 'generators': [56566145405, 75258822112, 490654080, 3669120, 81485883071], 'label': '2688.ed.84.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.n1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282400
    {'ambient': '2688.ed', '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', 'complements': ['2688.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '7.a1', '8.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6169, 2598, 5096, 4503], 'generators': [56577758221, 63283818170, 1122, 3669120, 69020185890, 81474230591, 56566145405, 11652480, 81474226495], 'label': '2688.ed.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1256'}
  • id: 182282401
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11307', 'aut_weyl_index': 8, 'centralizer': '336.a1', 'complements': ['448.c1', '448.g1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.d1', '42.a1', '48.b1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3351, 4505, 2996, 5533], 'generators': [81474226495, 69020185890, 56566145405, 3669120, 81953228095, 57045185723, 81474230591], 'label': '2688.ed.6.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1', '3.a1'], 'normal_contains': ['12.a1', '12.b1', '42.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '672.1256', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 182282402
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 168, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.e1', '42.f1'], 'contains': ['168.k1', '168.l1', '168.o1', '168.p1', '168.z1', '168.bf1'], 'core': '336.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [8726, -1, 8999, -1], 'generators': [56566145405, 56577757565, 81964884671, 3669120, 81485883071], 'label': '2688.ed.84.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.i1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282403
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.27', 'aut_weyl_index': 336, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['42.d1', '42.f1'], 'contains': ['168.k1', '168.m1', '168.p1', '168.ba1', '168.bg1'], 'core': '672.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [8885, -1, 9169, -1], 'generators': [44123713615, 56566145405, 81964884671, 3669120, 81485883071], 'label': '2688.ed.84.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.j1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282404
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.e1', '42.a1', '42.d1', '42.f1'], 'contains': ['168.f1', '168.h1', '168.k1', '168.n1', '168.w1', '168.bc1'], 'core': '672.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5442, -1, 4681, -1], 'generators': [56566145405, 479001600, 3669120, 75726251872, 81474230591], 'label': '2688.ed.84.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.k1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282405
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '84.l1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.f1', '42.b1', '42.e1', '42.f1'], 'contains': ['168.l1', '168.m1', '168.n1', '168.x1', '168.bd1'], 'core': '336.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [9180, -1, 8322, -1], 'generators': [56566145405, 56577757565, 479001600, 3669120, 81474230591], 'label': '2688.ed.84.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.l1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.l1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282406
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '84.m1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.g1', '42.b1', '42.d1'], 'contains': ['168.m1', '168.n1', '168.y1', '168.be1'], 'core': '672.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8227, -1, 7475, -1], 'generators': [56566145405, 75258822112, 479001600, 3669120, 81474230591], 'label': '2688.ed.84.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.m1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.m1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282412
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11307', 'aut_weyl_index': 8, 'centralizer': '336.b1', 'complements': ['448.c1', '448.g1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.c1', '42.b1', '48.c1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7315, 2480, 4889, 7017], 'generators': [81474226495, 69020185890, 56577758221, 56566145405, 3669120, 81953228095, 81474230591], 'label': '2688.ed.6.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1', 'normal_contained_in': ['2.b1', '3.a1'], 'normal_contains': ['12.a1', '12.c1', '42.b1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '672.1256', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 182282413
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '84.s1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.11', 'aut_weyl_index': 672, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['42.f1', '42.g1'], 'contains': ['168.w1', '168.x1', '168.z1', '168.ba1', '168.bf1', '168.bg1'], 'core': '672.c1', 'coset_action_label': None, 'count': 84, 'diagramx': [9890, -1, 9338, -1], 'generators': [56566145405, 56577757565, 69031838370, 81964884671, 3669120], 'label': '2688.ed.84.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.s1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282414
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '84.t1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.5', 'aut_weyl_index': 896, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.m1', '42.b1', '42.g1'], 'contains': ['168.x1', '168.y1', '168.bb1', '168.bd1', '168.be1'], 'core': '672.c1', 'coset_action_label': None, 'count': 14, 'diagramx': [9032, -1, 7814, -1], 'generators': [56566145405, 75258822112, 3669120, 69499187490, 81474230591], 'label': '2688.ed.84.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.t1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.t1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282415
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '84.u1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.n1', '42.c1', '42.f1', '42.g1'], 'contains': ['168.z1', '168.ba1', '168.bc1', '168.bd1'], 'core': '672.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [9326, -1, 8152, -1], 'generators': [56566145405, 56577757565, 69031838370, 3669120, 81474230591], 'label': '2688.ed.84.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.u1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.u1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282416
    {'ambient': '2688.ed', 'aut_centralizer_order': 28, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '32.a1', '48.b1'], 'contains': ['192.a1', '192.c1', '672.d1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [690, -1, 384, -1], 'generators': [75247206450, 75726208050, 57045185723], 'label': '2688.ed.96.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '96.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282417
    {'ambient': '2688.ed', 'aut_centralizer_order': 224, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '32.b1', '48.b1', '48.c1'], 'contains': ['192.a1', '192.b1', '672.a1'], 'core': '672.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4425, -1, 3001, -1], 'generators': [81474226495, 3669120, 81953228095], 'label': '2688.ed.96.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '96.b1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282418
    {'ambient': '2688.ed', 'aut_centralizer_order': 56, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '32.c1', '48.b1', '48.d1'], 'contains': ['192.b1', '192.c1', '672.b1'], 'core': '672.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [4577, -1, 2647, -1], 'generators': [56566186381, 3669120, 44112104729], 'label': '2688.ed.96.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '96.c1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282419
    {'ambient': '2688.ed', 'aut_centralizer_order': 112, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '48.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '32.d1', '48.c1', '48.d1'], 'contains': ['192.b1', '672.c1'], 'core': '672.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [7176, -1, 5411, -1], 'generators': [56577758221, 3669120, 44112104729], 'label': '2688.ed.96.d1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '96.d1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282420
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1', '56.e1'], 'contains': ['224.a1', '224.b1', '224.d1', '224.l1', '224.n1', '336.e1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [1415, -1, 1226, -1], 'generators': [81474228973, 57045187785, 57045147465, 62793166108], 'label': '2688.ed.112.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '112.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282421
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.a1', '56.e1'], 'contains': ['224.a1', '224.c1', '224.d1', '224.m1', '224.n1', '336.f1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [2142, -1, 1477, -1], 'generators': [44591107668, 81474228973, 57045187785, 62796835228], 'label': '2688.ed.112.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '112.b1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282422
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.a1', '56.b1', '56.c1', '56.d1', '56.i1'], 'contains': ['224.o1', '336.i1', '448.a1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1117, -1, 1070, -1], 'generators': [62793166108, 56566145405, 44112103731, 63272165690], 'label': '2688.ed.112.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '112.c1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282423
    {'ambient': '2688.ed', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '1344.11307', 'aut_weyl_index': 8, 'centralizer': '672.a1', 'complements': ['448.a1', '448.g1', '448.c1', '448.f1'], 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.b1', '12.c1', '42.c1', '48.d1'], 'core': '6.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7144, 894, 4703, 8419], 'generators': [81474226495, 69020185890, 56577758221, 56566145405, 3669120, 11652480, 81474230591], 'label': '2688.ed.6.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1', 'normal_contained_in': ['2.c1', '3.a1'], 'normal_contains': ['12.b1', '12.c1', '42.c1'], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': '1344.11688', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '672.1256'}
  • id: 182282424
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '28.c1', '56.e1', '56.f1', '56.g1'], 'contains': ['224.a1', '224.e1', '224.f1', '336.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4292, -1, 4780, -1], 'generators': [81474228973, 57045187785, 57045147465, 3669120], 'label': '2688.ed.112.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.d1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282425
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.h1', '56.e1', '56.h1'], 'contains': ['224.b1', '224.c1', '224.e1', '224.g1', '224.h1', '336.k1'], 'core': '672.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3301, -1, 4145, -1], 'generators': [44112103731, 3669120, 75247209952, 63272165690], 'label': '2688.ed.112.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.e1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282426
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.e1', '56.e1', '56.f1', '56.j1'], 'contains': ['224.d1', '224.e1', '224.i1', '336.l1'], 'core': '672.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4608, -1, 5038, -1], 'generators': [75726247012, 3669120, 56566146266, 50818125854], 'label': '2688.ed.112.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.f1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282427
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '28.f1', '56.g1', '56.h1', '56.j1'], 'contains': ['224.e1', '224.j1', '336.b1'], 'core': '336.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [6741, -1, 6697, -1], 'generators': [44112103731, 11612160, 3669120, 63272165690], 'label': '2688.ed.112.g1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.g1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282428
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '112.h1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.g1', '56.f1', '56.h1'], 'contains': ['224.e1', '224.k1', '336.m1'], 'core': '672.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [6893, -1, 6026, -1], 'generators': [44112103731, 75258822112, 3669120, 63272165690], 'label': '2688.ed.112.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.h1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282429
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.k1', '56.e1', '56.l1'], 'contains': ['224.f1', '224.g1', '224.i1', '224.l1', '224.m1', '336.n1'], 'core': '672.b1', 'coset_action_label': None, 'count': 112, 'diagramx': [3447, -1, 3977, -1], 'generators': [1122, 56566145405, 56566185725, 3669120], 'label': '2688.ed.112.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.i1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282430
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '112.j1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.i1', '56.e1', '56.m1'], 'contains': ['224.f1', '224.h1', '224.i1', '224.n1', '336.o1'], 'core': '672.b1', 'coset_action_label': None, 'count': 112, 'diagramx': [3701, -1, 4612, -1], 'generators': [75726206692, 75726247012, 3669120, 56566146266], 'label': '2688.ed.112.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.j1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282435
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '112.n1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.i1', '56.k1', '56.n1', '56.o1', '56.p1', '56.q1', '56.r1'], 'contains': ['224.o1', '336.u1', '448.b1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [4156, -1, 3690, -1], 'generators': [69020185890, 50339124835, 1122, 3669120], 'label': '2688.ed.112.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '112.n1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.n1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282436
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '112.o1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '56.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.m1', '56.h1', '56.m1'], 'contains': ['224.h1', '224.j1', '224.k1', '336.w1'], 'core': '672.c1', 'coset_action_label': None, 'count': 56, 'diagramx': [6590, -1, 6375, -1], 'generators': [81953231628, 56566142764, 75258822112, 3669120], 'label': '2688.ed.112.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.o1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282437
    {'ambient': '2688.ed', 'aut_centralizer_order': 12, 'aut_label': '112.p1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.n1', '56.j1', '56.l1', '56.m1'], 'contains': ['224.i1', '224.j1', '336.y1'], 'core': '672.c1', 'coset_action_label': None, 'count': 112, 'diagramx': [6134, -1, 7075, -1], 'generators': [1122, 56577797885, 11612160, 3669120], 'label': '2688.ed.112.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '112.p1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282438
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '112.q1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.a1', '56.k1', '56.s1', '56.t1', '56.u1'], 'contains': ['224.o1', '336.bc1', '448.c1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [954, -1, 691, -1], 'generators': [69020185890, 50339124835, 40320, 1122], 'label': '2688.ed.112.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '112.q1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.q1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282439
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '112.r1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1', '56.r1', '56.s1'], 'contains': ['224.o1', '336.bh1', '448.e1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2385, -1, 1950, -1], 'generators': [69020185890, 50339124835, 56569814525, 1122], 'label': '2688.ed.112.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '112.r1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.r1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282440
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '112.s1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.b1', '56.d1', '56.n1', '56.t1'], 'contains': ['224.o1', '336.bi1', '448.f1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1243, -1, 1763, -1], 'generators': [81953231628, 62793166108, 56566145405, 44112103731], 'label': '2688.ed.112.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '112.s1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.s1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282441
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '112.t1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.c1', '56.o1', '56.s1', '56.t1', '56.u1'], 'contains': ['224.o1', '336.bj1', '448.g1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1622, -1, 925, -1], 'generators': [69020185890, 50339124835, 1122, 56566185725], 'label': '2688.ed.112.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '112.t1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.t1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282442
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '112.u1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '56.d1', '56.r1', '56.u1'], 'contains': ['224.o1', '336.d1', '448.d1'], 'core': '336.d1', 'coset_action_label': None, 'count': 7, 'diagramx': [318, -1, 423, -1], 'generators': [69020185890, 1122, 56566145405, 81474230591], 'label': '2688.ed.112.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '112.u1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.u1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282443
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '168.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '64.a1', '64.b1', '64.c1'], 'contains': ['384.a1', '896.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [35, -1, 540, -1], 'generators': [81474226495, 1122], 'label': '2688.ed.128.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '128.a1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282444
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '168.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '21.a1', 'complements': ['16.d1'], 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '56.d1', '84.a1', '84.e1'], 'contains': ['336.d1', '336.i1', '336.bi1'], 'core': '168.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1449, 6064, 1646, 5411], 'generators': [69020185890, 56566145405, 479001600, 81474230591], 'label': '2688.ed.168.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '168.a1', 'normal_contained_in': ['24.a1', '84.a1'], 'normal_contains': ['336.d1', '1344.a1'], 'normalizer': '1.a1', 'old_label': '168.a1', 'projective_image': '1344.11307', 'quotient_action_image': '21.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '168.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282445
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '168.b1', 'complements': ['336.c1', '336.p1', '336.y1', '336.z1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.d1'], 'contains': ['16.a1', '24.a1', '56.d1', '64.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1102, 8896, 743, 1196], 'generators': [81474226495, 69020185890, 1122, 56566145405, 63272165690, 81474230591], 'label': '2688.ed.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '24.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '1344.11307', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282446
    {'ambient': '2688.ed', 'aut_centralizer_order': 168, 'aut_label': '168.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 168, 'centralizer': '4.a1', 'complements': ['16.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '56.g1', '84.h1'], 'contains': ['336.a1', '336.b1', '336.c1'], 'core': '168.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7513, 8273, 7479, 7138], 'generators': [11612160, 490654080, 3669120, 11652480], 'label': '2688.ed.168.b1', 'mobius_quo': 0, 'mobius_sub': -56, 'normal_closure': '168.b1', 'normal_contained_in': ['21.a1'], 'normal_contains': ['336.a1', '336.b1', '336.c1'], 'normalizer': '1.a1', 'old_label': '168.b1', 'projective_image': '672.1256', 'quotient_action_image': '1.1', 'quotient_action_kernel': '168.43', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '168.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282447
    {'ambient': '2688.ed', 'aut_centralizer_order': 512, 'aut_label': '168.c1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '21.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '56.r1', '84.a1', '84.b1', '84.c1'], 'contains': ['336.d1', '336.u1', '336.bh1'], 'core': '168.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3104, 4588, 2628, 6246], 'generators': [69020185890, 56566145405, 3669120, 81474230591], 'label': '2688.ed.168.c1', 'mobius_quo': 1, 'mobius_sub': -56, 'normal_closure': '168.c1', 'normal_contained_in': ['24.b1', '84.a1', '84.b1', '84.c1'], 'normal_contains': ['336.d1', '1344.b1'], 'normalizer': '1.a1', 'old_label': '168.c1', 'projective_image': '1344.11688', 'quotient_action_image': '21.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '168.c1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282448
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.d1', '84.g1'], 'contains': ['336.e1', '336.f1', '336.g1', '336.h1', '336.j1', '336.ba1', '336.bb1', '336.bd1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [3402, -1, 3357, -1], 'generators': [57045187325, 81477899711, 56566145405, 479001600], 'label': '2688.ed.168.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '168.d1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282449
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.a1', '84.d1', '84.e1', '84.g1'], 'contains': ['336.e1', '336.h1', '336.i1', '336.bb1', '336.bc1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2304, -1, 2277, -1], 'generators': [57045187325, 56566145405, 479001600, 81474230591], 'label': '2688.ed.168.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '168.e1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282450
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.d1', '84.k1'], 'contains': ['336.g1', '336.h1', '336.j1', '336.bf1', '336.bg1', '336.bk1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [4646, -1, 3445, -1], 'generators': [81477899711, 56566145405, 479001600, 75726251872], 'label': '2688.ed.168.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '168.f1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282451
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.b1', '84.a1', '84.d1'], 'contains': ['336.g1', '336.i1', '336.be1', '336.bh1', '336.bi1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2767, -1, 2540, -1], 'generators': [69023855010, 56566145405, 479001600, 81474230591], 'label': '2688.ed.168.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.g1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282452
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.c1', '84.d1', '84.e1', '84.k1'], 'contains': ['336.h1', '336.i1', '336.bg1', '336.bj1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2590, -1, 2364, -1], 'generators': [56566145405, 479001600, 75726251872, 81474230591], 'label': '2688.ed.168.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '168.h1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282532
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '336.y1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '28.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.p1', '168.o1', '168.u1', '168.v1', '168.z1', '168.bf1'], 'contains': ['672.c1', '672.j1'], 'core': '672.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [8612, -1, 7825, -1], 'generators': [56577797885, 11612160, 3669120], 'label': '2688.ed.336.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.y1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282453
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.e1', '84.f1', '84.g1', '84.h1'], 'contains': ['336.a1', '336.e1', '336.f1', '336.k1', '336.l1', '336.n1', '336.o1'], 'core': '336.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6017, -1, 5706, -1], 'generators': [57045187325, 56566145405, 479001600, 3669120], 'label': '2688.ed.168.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.i1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282454
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '32.27', 'aut_weyl_index': 336, 'centralizer': '28.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.f1', '84.f1', '84.h1'], 'contains': ['336.a1', '336.l1', '336.m1', '336.p1'], 'core': '336.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7676, -1, 7626, -1], 'generators': [56577757565, 490654080, 3669120, 11652480], 'label': '2688.ed.168.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.j1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282455
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['84.f1', '84.g1', '84.i1', '84.j1', '84.k1'], 'contains': ['336.h1', '336.j1', '336.k1', '336.l1', '336.r1', '336.v1'], 'core': '672.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [6634, -1, 7361, -1], 'generators': [50818166755, 56566145405, 479001600, 3669120], 'label': '2688.ed.168.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.k1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282456
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '8.b1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '168.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '24.b1', '56.r1', '64.b1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2953, 7025, 2660, 2542], 'generators': [81474226495, 69020185890, 1122, 56566145405, 3669120, 81474230591], 'label': '2688.ed.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '24.b1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282457
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.h1', '84.h1', '84.i1', '84.l1'], 'contains': ['336.b1', '336.k1', '336.m1', '336.s1', '336.w1'], 'core': '336.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [8870, -1, 8392, -1], 'generators': [56566145405, 56577757565, 479001600, 3669120], 'label': '2688.ed.168.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.l1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282458
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '168.m1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.f1', '84.j1', '84.l1', '84.m1'], 'contains': ['336.k1', '336.m1', '336.t1', '336.x1'], 'core': '672.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9016, -1, 8876, -1], 'generators': [56566145405, 50350736995, 479001600, 3669120], 'label': '2688.ed.168.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.m1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282459
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '168.n1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.i1', '84.a1', '84.g1', '84.k1', '84.l1', '84.m1'], 'contains': ['336.g1', '336.i1', '336.k1', '336.q1', '336.u1'], 'core': '672.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5675, -1, 4909, -1], 'generators': [56566145405, 479001600, 3669120, 81474230591], 'label': '2688.ed.168.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.n1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.n1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282460
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '168.o1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.138', 'aut_weyl_index': 168, 'centralizer': '28.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.j1', '84.h1', '84.i1'], 'contains': ['336.b1', '336.l1', '336.y1'], 'core': '336.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [7876, -1, 7773, -1], 'generators': [57056799485, 56577797885, 11612160, 3669120], 'label': '2688.ed.168.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.o1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282461
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '168.p1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.27', 'aut_weyl_index': 336, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['84.f1', '84.i1', '84.j1'], 'contains': ['336.l1', '336.m1', '336.z1'], 'core': '672.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [8733, -1, 9642, -1], 'generators': [57056799485, 56577797885, 81485842751, 3669120], 'label': '2688.ed.168.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.p1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282462
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.q1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.g1', '84.n1', '84.o1', '84.q1'], 'contains': ['336.n1', '336.o1', '336.q1', '336.r1', '336.v1', '336.bb1', '336.bd1'], 'core': '672.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [7043, -1, 6869, -1], 'generators': [57045187325, 56566145405, 81953232191, 3669120], 'label': '2688.ed.168.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.q1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282463
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '168.r1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['84.f1', '84.n1', '84.p1', '84.q1', '84.r1'], 'contains': ['336.n1', '336.p1', '336.r1', '336.t1', '336.z1'], 'core': '672.b1', 'coset_action_label': None, 'count': 168, 'diagramx': [8150, -1, 8718, -1], 'generators': [56566145405, 50350736995, 3669120, 11652480], 'label': '2688.ed.168.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.r1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282464
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '168.s1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.k1', '84.b1', '84.g1', '84.o1', '84.p1', '84.r1'], 'contains': ['336.n1', '336.r1', '336.u1', '336.ba1', '336.bc1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [5562, -1, 4396, -1], 'generators': [56566145405, 56566185725, 3669120, 81474230591], 'label': '2688.ed.168.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.s1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.s1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282465
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '168.t1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1344, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['84.f1', '84.n1', '84.q1'], 'contains': ['336.o1', '336.p1', '336.v1', '336.x1', '336.z1'], 'core': '672.b1', 'coset_action_label': None, 'count': 168, 'diagramx': [8569, -1, 9034, -1], 'generators': [75258822112, 56577797885, 490654080, 3669120], 'label': '2688.ed.168.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.t1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282466
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '168.u1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '28.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.l1', '84.h1', '84.q1', '84.r1'], 'contains': ['336.c1', '336.n1', '336.p1', '336.s1', '336.y1'], 'core': '336.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [8278, -1, 7919, -1], 'generators': [56566145405, 56577757565, 3669120, 11652480], 'label': '2688.ed.168.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.u1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282467
    {'ambient': '2688.ed', 'aut_centralizer_order': 1, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1344.4277', 'aut_weyl_index': 8, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['16.b1', '16.c1', '16.d1', '24.c1', '56.g1'], 'core': '168.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [6404, -1, 5172, -1], 'generators': [56577758221, 3669120, 44112104729, 44602756683, 11652480, 69020185045], 'label': '2688.ed.8.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '8.c1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 182282468
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '168.v1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '16.11', 'aut_weyl_index': 672, 'centralizer': '28.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.m1', '84.h1', '84.q1'], 'contains': ['336.c1', '336.o1', '336.p1', '336.w1', '336.y1'], 'core': '336.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [8441, -1, 8067, -1], 'generators': [56577797885, 11612160, 490654080, 3669120], 'label': '2688.ed.168.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.v1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282469
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.w1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.k1', '84.n1', '84.o1', '84.s1'], 'contains': ['336.q1', '336.r1', '336.v1', '336.bg1', '336.bk1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [7269, -1, 6957, -1], 'generators': [56566145405, 81953232191, 3669120, 75726251872], 'label': '2688.ed.168.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.w1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282470
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '168.x1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['84.l1', '84.q1', '84.s1', '84.t1'], 'contains': ['336.q1', '336.s1', '336.t1', '336.w1', '336.x1'], 'core': '672.c1', 'coset_action_label': None, 'count': 42, 'diagramx': [9965, -1, 9338, -1], 'generators': [56566145405, 50350736995, 81953232191, 3669120], 'label': '2688.ed.168.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.x1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282471
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '168.y1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['84.m1', '84.n1', '84.t1'], 'contains': ['336.q1', '336.t1', '336.x1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 42, 'diagramx': [9162, -1, 8561, -1], 'generators': [56566145405, 75258822112, 81953232191, 3669120], 'label': '2688.ed.168.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.y1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282473
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '168.ba1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['84.j1', '84.n1', '84.p1', '84.s1', '84.u1'], 'contains': ['336.r1', '336.t1', '336.z1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 168, 'diagramx': [9426, -1, 9495, -1], 'generators': [56566145405, 75258822112, 3669120, 81485883071], 'label': '2688.ed.168.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.ba1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282474
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '168.bb1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.n1', '84.a1', '84.o1', '84.t1'], 'contains': ['336.q1', '336.u1', '336.be1', '336.bi1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [4870, -1, 3807, -1], 'generators': [56566145405, 3669120, 69499187490, 81474230591], 'label': '2688.ed.168.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.bb1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bb1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282475
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '168.bc1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.o1', '84.b1', '84.k1', '84.o1', '84.p1', '84.u1'], 'contains': ['336.r1', '336.u1', '336.bf1', '336.bj1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [5486, -1, 4483, -1], 'generators': [75247250272, 56566145405, 3669120, 81474230591], 'label': '2688.ed.168.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.bc1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bc1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282476
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '168.bd1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.p1', '84.c1', '84.l1', '84.r1', '84.t1', '84.u1'], 'contains': ['336.s1', '336.t1', '336.u1'], 'core': '672.c1', 'coset_action_label': None, 'count': 14, 'diagramx': [9819, -1, 8224, -1], 'generators': [56566145405, 56577757565, 3669120, 81474230591], 'label': '2688.ed.168.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.bd1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bd1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282477
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '168.be1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.q1', '84.c1', '84.m1', '84.p1', '84.t1'], 'contains': ['336.t1', '336.u1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [8013, -1, 7233, -1], 'generators': [56566145405, 75258822112, 3669120, 81474230591], 'label': '2688.ed.168.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '168.be1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.be1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282478
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.d1'], 'contains': ['16.a1', '24.d1', '56.u1', '64.c1'], 'core': '16.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [427, -1, 398, -1], 'generators': [81474226495, 69020185890, 1122, 56566145405, 56566186381, 81474230591], 'label': '2688.ed.8.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.d1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282479
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '168.bf1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.11', 'aut_weyl_index': 672, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.i1', '84.q1', '84.s1'], 'contains': ['336.v1', '336.w1', '336.y1', '336.z1'], 'core': '672.c1', 'coset_action_label': None, 'count': 84, 'diagramx': [9682, -1, 9789, -1], 'generators': [57056799485, 69031838370, 11612160, 3669120], 'label': '2688.ed.168.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.bf1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282480
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '168.bg1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1344, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['84.j1', '84.n1', '84.s1'], 'contains': ['336.v1', '336.x1', '336.z1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 168, 'diagramx': [9299, -1, 9936, -1], 'generators': [57056799485, 69031838370, 81485842751, 3669120], 'label': '2688.ed.168.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.bg1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282481
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.bh1', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['84.d1', '84.o1'], 'contains': ['336.ba1', '336.bb1', '336.bd1', '336.be1', '336.bf1', '336.bg1', '336.bk1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [4722, -1, 3533, -1], 'generators': [57045187325, 81477899711, 56566145405, 69499187490], 'label': '2688.ed.168.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '168.bh1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282482
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '168.bi1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.s1', '84.b1', '84.d1'], 'contains': ['336.ba1', '336.bc1', '336.bf1', '336.bh1', '336.bj1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2891, -1, 2452, -1], 'generators': [69023855010, 56566145405, 56566185725, 81474230591], 'label': '2688.ed.168.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '168.bi1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bi1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282483
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '168.bj1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['56.t1', '84.d1', '84.e1', '84.o1'], 'contains': ['336.bb1', '336.bc1', '336.bg1', '336.bi1', '336.bj1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [1915, -1, 2067, -1], 'generators': [57045187325, 56566145405, 69499187490, 81474230591], 'label': '2688.ed.168.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '168.bj1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bj1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282484
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '168.bk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '56.u1', '84.b1', '84.e1'], 'contains': ['336.d1', '336.bc1', '336.bj1'], 'core': '336.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [1177, -1, 808, -1], 'generators': [69020185890, 56566145405, 56566185725, 81474230591], 'label': '2688.ed.168.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '168.bk1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.bk1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282485
    {'ambient': '2688.ed', 'aut_centralizer_order': 224, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '64.a1', '96.a1', '96.b1'], 'contains': ['384.a1', '1344.a1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [391, -1, 637, -1], 'generators': [81474226495, 81953228095], 'label': '2688.ed.192.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '192.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282486
    {'ambient': '2688.ed', 'aut_centralizer_order': 448, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '64.b1', '96.b1', '96.c1', '96.d1'], 'contains': ['384.a1', '1344.b1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5286, -1, 2824, -1], 'generators': [81474226495, 3669120], 'label': '2688.ed.192.b1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '192.b1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282487
    {'ambient': '2688.ed', 'aut_centralizer_order': 56, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '64.c1', '96.a1', '96.c1'], 'contains': ['384.a1', '1344.c1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [131, -1, 423, -1], 'generators': [56566186381, 44112104729], 'label': '2688.ed.192.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '192.c1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282488
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.a1', '56.a1', '112.a1', '112.b1', '112.d1'], 'contains': ['448.a1', '448.c1', '672.d1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [634, -1, 932, -1], 'generators': [81474228973, 57045187785, 57045147465], 'label': '2688.ed.224.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '224.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282489
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '12.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '336.210', 'aut_weyl_index': 32, 'centralizer': '168.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.b1'], 'contains': ['24.a1', '24.b1', '84.a1', '96.b1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3259, 6292, 2996, 3847], 'generators': [81474226495, 69020185890, 56566145405, 3669120, 81953228095, 81474230591], 'label': '2688.ed.12.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1', '6.b1'], 'normal_contains': ['24.a1', '24.b1', '84.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282490
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '224.b1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.d1', '112.a1', '112.e1'], 'contains': ['448.a1', '448.d1', '448.f1', '672.e1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [994, -1, 1342, -1], 'generators': [44112103731, 75247209952, 63272165690], 'label': '2688.ed.224.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.b1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282491
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '224.c1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.b1', '112.b1', '112.e1'], 'contains': ['448.a1', '448.e1', '448.f1', '672.f1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1778, -1, 1966, -1], 'generators': [81953231628, 56566142764, 75250879072], 'label': '2688.ed.224.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.c1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282492
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.c1', '112.a1', '112.b1', '112.f1'], 'contains': ['448.a1', '448.g1', '672.g1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [2047, -1, 1634, -1], 'generators': [75726247012, 56566146266, 50818125854], 'label': '2688.ed.224.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '224.d1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282493
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '56.i1', '112.d1', '112.e1', '112.f1', '112.g1', '112.h1'], 'contains': ['448.a1', '448.b1', '672.a1'], 'core': '672.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4183, -1, 4783, -1], 'generators': [44112103731, 3669120, 63272165690], 'label': '2688.ed.224.e1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.e1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282494
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '224.f1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.c1', '56.k1', '112.d1', '112.i1', '112.j1', '112.k1', '112.l1'], 'contains': ['448.b1', '448.c1', '672.b1'], 'core': '672.b1', 'coset_action_label': None, 'count': 112, 'diagramx': [3889, -1, 4637, -1], 'generators': [40320, 1122, 3669120], 'label': '2688.ed.224.f1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.f1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282495
    {'ambient': '2688.ed', 'aut_centralizer_order': 384, 'aut_label': '224.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.r1', '112.e1', '112.i1', '112.m1'], 'contains': ['448.b1', '448.d1', '448.e1', '672.h1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3220, -1, 4257, -1], 'generators': [1122, 56566145405, 3669120], 'label': '2688.ed.224.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.g1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282496
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '224.h1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.n1', '112.e1', '112.j1', '112.o1'], 'contains': ['448.b1', '448.f1', '672.i1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3740, -1, 4491, -1], 'generators': [81953231628, 56566142764, 3669120], 'label': '2688.ed.224.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.h1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282497
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '224.i1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.o1', '112.f1', '112.i1', '112.j1', '112.k1', '112.p1'], 'contains': ['448.b1', '448.g1', '672.j1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 112, 'diagramx': [4342, -1, 4928, -1], 'generators': [1122, 56566185725, 3669120], 'label': '2688.ed.224.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.i1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282498
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '224.j1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.d1', '56.p1', '112.g1', '112.l1', '112.m1', '112.o1', '112.p1'], 'contains': ['448.b1', '672.c1'], 'core': '672.c1', 'coset_action_label': None, 'count': 56, 'diagramx': [6406, -1, 6375, -1], 'generators': [1122, 11612160, 3669120], 'label': '2688.ed.224.j1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.j1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282499
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '224.k1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['56.q1', '112.h1', '112.k1', '112.m1', '112.o1'], 'contains': ['448.b1', '672.k1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 56, 'diagramx': [6713, -1, 6026, -1], 'generators': [1122, 56577757565, 3669120], 'label': '2688.ed.224.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '224.k1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282500
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '12.b1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '336.210', 'aut_weyl_index': 32, 'centralizer': '336.a1', 'complements': ['224.a1', '224.n1', '224.d1'], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.a1', '6.c1'], 'contains': ['24.b1', '24.d1', '84.b1', '96.c1'], 'core': '12.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3079, 4863, 2488, 5111], 'generators': [81474226495, 69020185890, 56566145405, 56566186381, 3669120, 81474230591], 'label': '2688.ed.12.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1', 'normal_contained_in': ['4.b1', '6.a1', '6.c1'], 'normal_contains': ['24.b1', '84.b1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '1344.11688', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 182282501
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '224.l1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.u1', '112.a1', '112.i1'], 'contains': ['448.c1', '448.d1', '448.g1', '672.l1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [832, -1, 1196, -1], 'generators': [1122, 56566145405, 56566185725], 'label': '2688.ed.224.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '224.l1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282502
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '224.m1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.s1', '112.b1', '112.i1'], 'contains': ['448.c1', '448.e1', '448.g1', '672.m1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [2527, -1, 1779, -1], 'generators': [56569814525, 40320, 1122], 'label': '2688.ed.224.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '224.m1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282503
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '224.n1', 'aut_quo_index': None, 'aut_stab_index': 448, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['56.t1', '112.a1', '112.b1', '112.j1'], 'contains': ['448.c1', '448.f1', '448.g1', '672.n1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 448, 'diagramx': [1333, -1, 1488, -1], 'generators': [44591107668, 81474228973, 57045187785], 'label': '2688.ed.224.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '224.n1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282504
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '224.o1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1', '112.n1', '112.q1', '112.r1', '112.s1', '112.t1', '112.u1'], 'contains': ['672.r1', '896.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [537, -1, 1085, -1], 'generators': [69020185890, 50339124835, 1122], 'label': '2688.ed.224.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '224.o1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.o1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282505
    {'ambient': '2688.ed', 'aut_centralizer_order': 672, 'aut_label': '336.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '2.a1', 'complements': ['8.d1'], 'conjugacy_class_count': 2, 'contained_in': ['48.b1', '112.d1', '168.b1', '168.i1', '168.j1'], 'contains': ['672.a1', '672.b1', '672.d1'], 'core': '336.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5681, 9271, 5619, 8022], 'generators': [479001600, 3669120, 479041920], 'label': '2688.ed.336.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '336.a1', 'normal_contained_in': ['42.a1', '168.b1'], 'normal_contains': ['672.a1', '672.b1'], 'normalizer': '1.a1', 'old_label': '336.a1', 'projective_image': '672.1256', 'quotient_action_image': '2.1', 'quotient_action_kernel': '168.43', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '336.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282506
    {'ambient': '2688.ed', 'aut_centralizer_order': 1344, 'aut_label': '336.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '2.b1', 'complements': ['8.d1'], 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '112.g1', '168.b1', '168.l1', '168.o1'], 'contains': ['672.a1', '672.c1'], 'core': '336.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7762, 8273, 7221, 7138], 'generators': [11612160, 479001600, 3669120], 'label': '2688.ed.336.b1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '336.b1', 'normal_contained_in': ['42.b1', '168.b1'], 'normal_contains': ['672.a1', '672.c1'], 'normalizer': '1.a1', 'old_label': '336.b1', 'projective_image': '672.1256', 'quotient_action_image': '2.1', 'quotient_action_kernel': '168.43', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '336.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282507
    {'ambient': '2688.ed', 'aut_centralizer_order': 336, 'aut_label': '336.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '4.a1', 'complements': ['8.a1', '8.d1'], 'conjugacy_class_count': 4, 'contained_in': ['48.d1', '112.l1', '168.b1', '168.u1', '168.v1'], 'contains': ['672.b1', '672.c1'], 'core': '336.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7478, 7319, 7110, 6295], 'generators': [11612160, 3669120, 11652480], 'label': '2688.ed.336.c1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '336.c1', 'normal_contained_in': ['42.c1', '168.b1'], 'normal_contains': ['672.b1', '672.c1'], 'normalizer': '1.a1', 'old_label': '336.c1', 'projective_image': '1344.11688', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.210', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282508
    {'ambient': '2688.ed', 'aut_centralizer_order': 512, 'aut_label': '336.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '21.a1', 'complements': ['8.c1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '112.u1', '168.a1', '168.c1', '168.bk1'], 'contains': ['672.r1'], 'core': '336.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1264, 6064, 775, 5411], 'generators': [69020185890, 56566145405, 81474230591], 'label': '2688.ed.336.d1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '336.d1', 'normal_contained_in': ['48.a1', '168.a1', '168.c1'], 'normal_contains': ['2688.a1'], 'normalizer': '1.a1', 'old_label': '336.d1', 'projective_image': '2688.ed', 'quotient_action_image': '21.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '336.d1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282509
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.a1', '168.d1', '168.e1', '168.i1'], 'contains': ['672.d1', '672.e1', '672.g1', '672.l1', '672.n1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2454, -1, 3133, -1], 'generators': [57045187325, 56566145405, 479001600], 'label': '2688.ed.336.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '336.e1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282510
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.b1', '168.d1', '168.i1'], 'contains': ['672.d1', '672.f1', '672.g1', '672.m1', '672.n1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3371, -1, 3221, -1], 'generators': [57045187325, 56569814525, 479001600], 'label': '2688.ed.336.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '336.f1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282511
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1344.11307', 'aut_weyl_index': 8, 'centralizer': '336.a1', 'complements': ['1344.c1', '1344.g1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.d1', '6.a1', '14.b1', '16.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3351, 6045, 2996, 2217], 'generators': [81474226495, 69020185890, 57045187785, 1122, 56566145405, 3669120, 63272165690, 81474230591], 'label': '2688.ed.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '672.1256', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 182282512
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '336.210', 'aut_weyl_index': 32, 'centralizer': '336.b1', 'complements': ['224.a1', '224.n1', '224.d1'], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.b1', '6.c1'], 'contains': ['24.b1', '84.c1', '96.d1'], 'core': '12.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [7239, 3176, 4928, 6295], 'generators': [81474226495, 69020185890, 56577758221, 56566145405, 3669120, 81474230591], 'label': '2688.ed.12.c1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1', 'normal_contained_in': ['4.c1', '6.b1', '6.c1'], 'normal_contains': ['24.b1', '84.c1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '1344.11688', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 182282513
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['168.d1', '168.f1', '168.g1', '168.n1'], 'contains': ['672.e1', '672.f1', '672.o1', '672.p1', '672.s1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [3623, -1, 3660, -1], 'generators': [81477899711, 56566145405, 479001600], 'label': '2688.ed.336.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.g1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282514
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '336.h1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.d1', '168.e1', '168.f1', '168.h1', '168.k1'], 'contains': ['672.e1', '672.g1', '672.q1', '672.u1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [3448, -1, 3397, -1], 'generators': [50818166755, 56566145405, 479001600], 'label': '2688.ed.336.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '336.h1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282515
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['112.c1', '168.a1', '168.e1', '168.g1', '168.h1', '168.n1'], 'contains': ['672.e1', '672.p1', '672.r1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2145, -1, 2428, -1], 'generators': [56566145405, 479001600, 81474230591], 'label': '2688.ed.336.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.i1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282516
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.d1', '168.f1', '168.k1'], 'contains': ['672.f1', '672.g1', '672.t1', '672.u1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [4956, -1, 3748, -1], 'generators': [50818166755, 56569814525, 479001600], 'label': '2688.ed.336.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '336.j1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282517
    {'ambient': '2688.ed', 'aut_centralizer_order': 768, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.e1', '168.i1', '168.k1', '168.l1', '168.m1', '168.n1'], 'contains': ['672.a1', '672.e1', '672.f1', '672.h1', '672.i1'], 'core': '672.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5931, -1, 5794, -1], 'generators': [56566145405, 479001600, 3669120], 'label': '2688.ed.336.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.k1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282518
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['112.f1', '168.i1', '168.j1', '168.k1', '168.o1', '168.p1'], 'contains': ['672.a1', '672.g1', '672.j1'], 'core': '672.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6123, -1, 6844, -1], 'generators': [57045187325, 479001600, 3669120], 'label': '2688.ed.336.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.l1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282519
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.h1', '168.j1', '168.l1', '168.m1', '168.p1'], 'contains': ['672.a1', '672.k1'], 'core': '672.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8515, -1, 7626, -1], 'generators': [56577757565, 479001600, 3669120], 'label': '2688.ed.336.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.m1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282520
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '336.n1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.i1', '168.i1', '168.q1', '168.r1', '168.s1', '168.u1'], 'contains': ['672.b1', '672.h1', '672.j1', '672.l1', '672.m1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [5855, -1, 5706, -1], 'generators': [56566145405, 56566185725, 3669120], 'label': '2688.ed.336.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.n1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282521
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '336.o1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.j1', '168.i1', '168.q1', '168.t1', '168.v1'], 'contains': ['672.b1', '672.i1', '672.j1', '672.n1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [6198, -1, 6554, -1], 'generators': [57045147005, 57045187325, 3669120], 'label': '2688.ed.336.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.o1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282522
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '336.p1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '28.h1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['112.k1', '168.j1', '168.r1', '168.t1', '168.u1', '168.v1'], 'contains': ['672.b1', '672.j1', '672.k1'], 'core': '672.b1', 'coset_action_label': None, 'count': 56, 'diagramx': [8293, -1, 7515, -1], 'generators': [56577757565, 3669120, 11652480], 'label': '2688.ed.336.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.p1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282523
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '336.210', 'aut_weyl_index': 32, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '6.a1'], 'contains': ['24.a1', '24.d1', '84.e1', '96.a1'], 'core': '24.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1298, -1, 570, -1], 'generators': [81474226495, 69020185890, 56566145405, 81953228095, 57045185723, 81474230591], 'label': '2688.ed.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.d1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282524
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '336.q1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.n1', '168.q1', '168.w1', '168.x1', '168.y1', '168.bb1'], 'contains': ['672.h1', '672.i1', '672.p1', '672.s1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [6275, -1, 6466, -1], 'generators': [56566145405, 81953232191, 3669120], 'label': '2688.ed.336.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.q1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282525
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '336.r1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.k1', '168.q1', '168.r1', '168.s1', '168.w1', '168.z1', '168.ba1', '168.bc1'], 'contains': ['672.h1', '672.j1', '672.q1', '672.t1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [6660, -1, 6756, -1], 'generators': [56566145405, 50339165155, 3669120], 'label': '2688.ed.336.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.r1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282526
    {'ambient': '2688.ed', 'aut_centralizer_order': 384, 'aut_label': '336.s1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['112.m1', '168.l1', '168.u1', '168.x1', '168.z1', '168.bd1'], 'contains': ['672.c1', '672.h1', '672.k1'], 'core': '672.c1', 'coset_action_label': None, 'count': 14, 'diagramx': [9411, -1, 7937, -1], 'generators': [56566145405, 56577757565, 3669120], 'label': '2688.ed.336.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.s1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282527
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '336.t1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '42.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['168.m1', '168.r1', '168.x1', '168.y1', '168.ba1', '168.bd1', '168.be1'], 'contains': ['672.h1', '672.k1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 42, 'diagramx': [9284, -1, 8561, -1], 'generators': [56566145405, 50350736995, 3669120], 'label': '2688.ed.336.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.t1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282528
    {'ambient': '2688.ed', 'aut_centralizer_order': 512, 'aut_label': '336.u1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.n1', '168.c1', '168.n1', '168.s1', '168.bb1', '168.bc1', '168.bd1', '168.be1'], 'contains': ['672.h1', '672.o1', '672.r1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [4808, -1, 4374, -1], 'generators': [56566145405, 3669120, 81474230591], 'label': '2688.ed.336.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.u1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.u1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282529
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '336.v1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.k1', '168.q1', '168.t1', '168.w1', '168.bf1', '168.bg1'], 'contains': ['672.i1', '672.j1', '672.u1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [7549, -1, 7743, -1], 'generators': [57045147005, 50818166755, 3669120], 'label': '2688.ed.336.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.v1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282533
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '336.z1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['168.p1', '168.r1', '168.t1', '168.z1', '168.ba1', '168.bf1', '168.bg1'], 'contains': ['672.j1', '672.k1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 168, 'diagramx': [9158, -1, 9180, -1], 'generators': [75258822112, 56577797885, 3669120], 'label': '2688.ed.336.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.z1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282534
    {'ambient': '2688.ed', 'aut_centralizer_order': 2, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '384.18159', 'aut_weyl_index': 28, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['7.a1'], 'contains': ['28.c1', '28.e1', '28.g1', '28.j1', '42.d1', '56.f1'], 'core': '336.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5116, -1, 5549, -1], 'generators': [75258822112, 63283818170, 62793166108, 44112103731, 3669120, 56566145405, 11652480], 'label': '2688.ed.14.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.a1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282535
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '336.ba1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.d1', '168.s1', '168.bh1', '168.bi1'], 'contains': ['672.l1', '672.m1', '672.o1', '672.q1', '672.t1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [4338, -1, 3572, -1], 'generators': [81477899711, 56566145405, 56566185725], 'label': '2688.ed.336.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '336.ba1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282536
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '336.bb1', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['168.d1', '168.e1', '168.q1', '168.bh1', '168.bj1'], 'contains': ['672.l1', '672.n1', '672.p1', '672.q1', '672.u1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [3020, -1, 3309, -1], 'generators': [57045187325, 56566145405, 81953232191], 'label': '2688.ed.336.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '336.bb1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282537
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '336.bc1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.q1', '168.e1', '168.s1', '168.bi1', '168.bj1', '168.bk1'], 'contains': ['672.l1', '672.q1', '672.r1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1666, -1, 2123, -1], 'generators': [56566145405, 56566185725, 81474230591], 'label': '2688.ed.336.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '336.bc1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bc1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282538
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '336.bd1', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['168.d1', '168.q1', '168.bh1'], 'contains': ['672.m1', '672.n1', '672.s1', '672.t1', '672.u1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [5031, -1, 4012, -1], 'generators': [57045187325, 56569814525, 81953232191], 'label': '2688.ed.336.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '336.bd1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282539
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '336.be1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['168.g1', '168.bb1', '168.bh1'], 'contains': ['672.o1', '672.p1', '672.s1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4247, -1, 3924, -1], 'generators': [81477899711, 56566145405, 69499187490], 'label': '2688.ed.336.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.be1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282540
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '336.bf1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.f1', '168.bc1', '168.bh1', '168.bi1'], 'contains': ['672.o1', '672.q1', '672.t1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [4661, -1, 3836, -1], 'generators': [75247250272, 81477899711, 56566145405], 'label': '2688.ed.336.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '336.bf1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282541
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '336.bg1', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['168.f1', '168.h1', '168.w1', '168.bh1', '168.bj1'], 'contains': ['672.p1', '672.q1', '672.u1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [3286, -1, 3485, -1], 'generators': [56566145405, 81953232191, 75726251872], 'label': '2688.ed.336.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '336.bg1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282542
    {'ambient': '2688.ed', 'aut_centralizer_order': 512, 'aut_label': '336.bh1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.r1', '168.c1', '168.g1', '168.bi1'], 'contains': ['672.o1', '672.r1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2793, -1, 2516, -1], 'generators': [69023855010, 56566145405, 81474230591], 'label': '2688.ed.336.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.bh1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bh1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282543
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '336.bi1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['112.s1', '168.a1', '168.g1', '168.bb1', '168.bj1'], 'contains': ['672.p1', '672.r1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1836, -1, 2299, -1], 'generators': [56566145405, 69499187490, 81474230591], 'label': '2688.ed.336.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '336.bi1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bi1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282544
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '336.bj1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.t1', '168.h1', '168.bc1', '168.bi1', '168.bj1', '168.bk1'], 'contains': ['672.q1', '672.r1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1998, -1, 2211, -1], 'generators': [75247250272, 56566145405, 81474230591], 'label': '2688.ed.336.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '336.bj1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bj1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282545
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '7.a1'], 'contains': ['28.a1', '28.b1', '28.c1', '28.e1', '28.h1', '28.i1', '28.k1', '42.a1', '56.e1'], 'core': '42.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3599, -1, 3528, -1], 'generators': [69020185890, 57045187785, 56566145405, 50339123205, 81953228201, 3669120, 81474230591], 'label': '2688.ed.14.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.b1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282546
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '336.bk1', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['168.f1', '168.w1', '168.bh1'], 'contains': ['672.s1', '672.t1', '672.u1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [5289, -1, 4100, -1], 'generators': [56569814525, 81953232191, 75726251872], 'label': '2688.ed.336.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '336.bk1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.bk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282547
    {'ambient': '2688.ed', 'aut_centralizer_order': 448, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '128.a1', '192.a1', '192.b1', '192.c1'], 'contains': ['2688.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [93, -1, 588, -1], 'generators': [81474226495], 'label': '2688.ed.384.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '384.a1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282548
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '448.a1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '112.c1', '224.a1', '224.b1', '224.c1', '224.d1', '224.e1'], 'contains': ['896.a1', '1344.a1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [980, -1, 1522, -1], 'generators': [44112103731, 63272165690], 'label': '2688.ed.448.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '448.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282549
    {'ambient': '2688.ed', 'aut_centralizer_order': 384, 'aut_label': '448.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1', '112.n1', '224.e1', '224.f1', '224.g1', '224.h1', '224.i1', '224.j1', '224.k1'], 'contains': ['896.a1', '1344.b1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3948, -1, 4637, -1], 'generators': [1122, 3669120], 'label': '2688.ed.448.b1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '448.b1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282550
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '448.c1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.c1', '112.q1', '224.a1', '224.f1', '224.l1', '224.m1', '224.n1'], 'contains': ['896.a1', '1344.c1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [912, -1, 1445, -1], 'generators': [40320, 1122], 'label': '2688.ed.448.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '448.c1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282551
    {'ambient': '2688.ed', 'aut_centralizer_order': 384, 'aut_label': '448.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.u1', '224.b1', '224.g1', '224.l1'], 'contains': ['896.a1', '1344.d1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [528, -1, 1599, -1], 'generators': [1122, 56566145405], 'label': '2688.ed.448.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '448.d1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282552
    {'ambient': '2688.ed', 'aut_centralizer_order': 384, 'aut_label': '448.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.r1', '224.c1', '224.g1', '224.m1'], 'contains': ['896.a1', '1344.e1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2576, -1, 2012, -1], 'generators': [56569814525, 1122], 'label': '2688.ed.448.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '448.e1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282553
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '448.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['112.s1', '224.b1', '224.c1', '224.h1', '224.n1'], 'contains': ['896.a1', '1344.f1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1475, -1, 1873, -1], 'generators': [81953231628, 56566142764], 'label': '2688.ed.448.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '448.f1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282554
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '448.g1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.t1', '224.d1', '224.i1', '224.l1', '224.m1', '224.n1'], 'contains': ['896.a1', '1344.g1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [1932, -1, 1676, -1], 'generators': [1122, 56566185725], 'label': '2688.ed.448.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.e1', 'old_label': '448.g1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282555
    {'ambient': '2688.ed', 'aut_centralizer_order': 5376, 'aut_label': '672.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '224.e1', '336.a1', '336.b1', '336.k1', '336.l1', '336.m1'], 'contains': ['1344.a1', '1344.b1'], 'core': '672.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5663, 9143, 5706, 7803], 'generators': [479001600, 3669120], 'label': '2688.ed.672.a1', 'mobius_quo': 2, 'mobius_sub': -112, 'normal_closure': '672.a1', 'normal_contained_in': ['84.a1', '336.a1', '336.b1'], 'normal_contains': ['1344.a1', '1344.b1'], 'normalizer': '1.a1', 'old_label': '672.a1', 'projective_image': '672.1256', 'quotient_action_image': '1.1', 'quotient_action_kernel': '672.1256', 'quotient_action_kernel_order': 672, 'quotient_fusion': None, 'short_label': '672.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282556
    {'ambient': '2688.ed', 'aut_centralizer_order': 2, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '768.1084716', 'aut_weyl_index': 14, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1'], 'contains': ['28.c1', '28.f1', '28.l1', '42.e1', '56.g1'], 'core': '168.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6050, -1, 6749, -1], 'generators': [63283818170, 62793166108, 56566145405, 44112103731, 56577757565, 3669120, 11652480], 'label': '2688.ed.14.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.c1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282557
    {'ambient': '2688.ed', 'aut_centralizer_order': 1344, 'aut_label': '672.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '2.a1', 'complements': ['4.d1'], 'conjugacy_class_count': 4, 'contained_in': ['96.c1', '224.f1', '336.a1', '336.c1', '336.n1', '336.o1', '336.p1'], 'contains': ['1344.b1', '1344.c1'], 'core': '672.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5451, 8391, 5619, 7138], 'generators': [40320, 3669120], 'label': '2688.ed.672.b1', 'mobius_quo': 0, 'mobius_sub': -112, 'normal_closure': '672.b1', 'normal_contained_in': ['84.b1', '336.a1', '336.c1'], 'normal_contains': ['1344.b1'], 'normalizer': '1.a1', 'old_label': '672.b1', 'projective_image': '1344.11688', 'quotient_action_image': '2.1', 'quotient_action_kernel': '336.210', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '672.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282558
    {'ambient': '2688.ed', 'aut_centralizer_order': 2688, 'aut_label': '672.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '2.b1', 'complements': ['4.d1'], 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '224.j1', '336.b1', '336.c1', '336.s1', '336.w1', '336.y1'], 'contains': ['1344.b1'], 'core': '672.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [7892, 7686, 7165, 6514], 'generators': [11612160, 3669120], 'label': '2688.ed.672.c1', 'mobius_quo': 0, 'mobius_sub': -112, 'normal_closure': '672.c1', 'normal_contained_in': ['84.c1', '336.b1', '336.c1'], 'normal_contains': ['1344.b1'], 'normalizer': '1.a1', 'old_label': '672.c1', 'projective_image': '1344.11688', 'quotient_action_image': '2.1', 'quotient_action_kernel': '336.210', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '672.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282559
    {'ambient': '2688.ed', 'aut_centralizer_order': 672, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.a1', '224.a1', '336.a1', '336.e1', '336.f1'], 'contains': ['1344.a1', '1344.c1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2259, -1, 2957, -1], 'generators': [479001600, 479041920], 'label': '2688.ed.672.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '336.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '672.d1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282560
    {'ambient': '2688.ed', 'aut_centralizer_order': 768, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['224.b1', '336.e1', '336.g1', '336.h1', '336.i1', '336.k1'], 'contains': ['1344.a1', '1344.d1', '1344.f1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2920, -1, 3133, -1], 'generators': [56566145405, 479001600], 'label': '2688.ed.672.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '672.e1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282561
    {'ambient': '2688.ed', 'aut_centralizer_order': 768, 'aut_label': '672.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['224.c1', '336.f1', '336.g1', '336.j1', '336.k1'], 'contains': ['1344.a1', '1344.e1', '1344.f1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3590, -1, 3660, -1], 'generators': [56569814525, 479001600], 'label': '2688.ed.672.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '672.f1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282562
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '672.g1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['224.d1', '336.e1', '336.f1', '336.h1', '336.j1', '336.l1'], 'contains': ['1344.a1', '1344.g1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3478, -1, 3309, -1], 'generators': [57045187325, 479001600], 'label': '2688.ed.672.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '672.g1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282563
    {'ambient': '2688.ed', 'aut_centralizer_order': 1536, 'aut_label': '672.h1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.g1', '336.k1', '336.n1', '336.q1', '336.r1', '336.s1', '336.t1', '336.u1'], 'contains': ['1344.b1', '1344.d1', '1344.e1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6165, -1, 5794, -1], 'generators': [56566145405, 3669120], 'label': '2688.ed.672.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '672.h1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282564
    {'ambient': '2688.ed', 'aut_centralizer_order': 768, 'aut_label': '672.i1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.h1', '336.k1', '336.o1', '336.q1', '336.v1', '336.w1', '336.x1'], 'contains': ['1344.b1', '1344.f1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6060, -1, 6466, -1], 'generators': [57045147005, 3669120], 'label': '2688.ed.672.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '672.i1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282565
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '672.j1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['224.i1', '336.l1', '336.n1', '336.o1', '336.p1', '336.r1', '336.v1', '336.y1', '336.z1'], 'contains': ['1344.b1', '1344.g1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [6555, -1, 6756, -1], 'generators': [56566185725, 3669120], 'label': '2688.ed.672.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '672.j1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282566
    {'ambient': '2688.ed', 'aut_centralizer_order': 384, 'aut_label': '672.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['224.k1', '336.m1', '336.p1', '336.s1', '336.t1', '336.w1', '336.x1', '336.z1'], 'contains': ['1344.b1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [8895, -1, 7937, -1], 'generators': [56577757565, 3669120], 'label': '2688.ed.672.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '672.k1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282567
    {'ambient': '2688.ed', 'aut_centralizer_order': 2, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '768.1084716', 'aut_weyl_index': 14, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1'], 'contains': ['28.e1', '28.f1', '28.n1', '42.f1', '56.j1'], 'core': '336.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [5854, -1, 7023, -1], 'generators': [69031838370, 81964884108, 56577757565, 62793166108, 3669120, 44112103731, 56566145405], 'label': '2688.ed.14.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.d1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282568
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '672.l1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['224.l1', '336.e1', '336.n1', '336.ba1', '336.bb1', '336.bc1'], 'contains': ['1344.c1', '1344.d1', '1344.g1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2843, -1, 3045, -1], 'generators': [56566145405, 56566185725], 'label': '2688.ed.672.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '672.l1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282569
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '672.m1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['224.m1', '336.f1', '336.n1', '336.ba1', '336.bd1'], 'contains': ['1344.c1', '1344.e1', '1344.g1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3846, -1, 3572, -1], 'generators': [56569814525, 56566185725], 'label': '2688.ed.672.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '672.m1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282570
    {'ambient': '2688.ed', 'aut_centralizer_order': 96, 'aut_label': '672.n1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['224.n1', '336.e1', '336.f1', '336.o1', '336.bb1', '336.bd1'], 'contains': ['1344.c1', '1344.f1', '1344.g1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [3173, -1, 3221, -1], 'generators': [57045147005, 57045187325], 'label': '2688.ed.672.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '672.n1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282571
    {'ambient': '2688.ed', 'aut_centralizer_order': 512, 'aut_label': '672.o1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.g1', '336.u1', '336.ba1', '336.be1', '336.bf1', '336.bh1'], 'contains': ['1344.d1', '1344.e1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3693, -1, 3748, -1], 'generators': [81477899711, 56566145405], 'label': '2688.ed.672.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '672.o1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282572
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '672.p1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['336.g1', '336.i1', '336.q1', '336.bb1', '336.be1', '336.bg1', '336.bi1'], 'contains': ['1344.d1', '1344.f1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [3061, -1, 3485, -1], 'generators': [56566145405, 81953232191], 'label': '2688.ed.672.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '672.p1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282573
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '672.q1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['336.h1', '336.r1', '336.ba1', '336.bb1', '336.bc1', '336.bf1', '336.bg1', '336.bj1'], 'contains': ['1344.d1', '1344.g1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [3257, -1, 3397, -1], 'generators': [56566145405, 50339165155], 'label': '2688.ed.672.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '672.q1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282574
    {'ambient': '2688.ed', 'aut_centralizer_order': 512, 'aut_label': '672.r1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.o1', '336.d1', '336.i1', '336.u1', '336.bc1', '336.bh1', '336.bi1', '336.bj1'], 'contains': ['1344.d1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2068, -1, 2299, -1], 'generators': [56566145405, 81474230591], 'label': '2688.ed.672.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '336.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '672.r1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.r1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282575
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '672.s1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['336.g1', '336.q1', '336.bd1', '336.be1', '336.bk1'], 'contains': ['1344.e1', '1344.f1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4707, -1, 4012, -1], 'generators': [56569814525, 81953232191], 'label': '2688.ed.672.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '672.s1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282576
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '672.t1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['336.j1', '336.r1', '336.ba1', '336.bd1', '336.bf1', '336.bk1'], 'contains': ['1344.e1', '1344.g1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [4902, -1, 3924, -1], 'generators': [56569814525, 50339165155], 'label': '2688.ed.672.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '672.t1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282577
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '672.u1', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['336.h1', '336.j1', '336.v1', '336.bb1', '336.bd1', '336.bg1', '336.bk1'], 'contains': ['1344.f1', '1344.g1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [3769, -1, 3836, -1], 'generators': [57045147005, 50818166755], 'label': '2688.ed.672.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1', 'old_label': '672.u1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282578
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '168.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '7.a1'], 'contains': ['28.f1', '28.g1', '28.h1', '28.m1', '28.o1', '42.b1', '56.h1'], 'core': '42.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6605, -1, 6102, -1], 'generators': [69020185890, 56566145405, 44112103731, 56577757565, 3669120, 81474230591, 63272165690], 'label': '2688.ed.14.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.e1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282579
    {'ambient': '2688.ed', 'aut_centralizer_order': 384, 'aut_label': '896.a1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '28.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '224.o1', '448.a1', '448.b1', '448.c1', '448.d1', '448.e1', '448.f1', '448.g1'], 'contains': ['2688.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1397, -1, 1638, -1], 'generators': [1122], 'label': '2688.ed.896.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '896.a1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '896.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282580
    {'ambient': '2688.ed', 'aut_centralizer_order': 5376, 'aut_label': '1344.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1', 'complements': ['2.c1'], 'conjugacy_class_count': 2, 'contained_in': ['192.a1', '448.a1', '672.a1', '672.d1', '672.e1', '672.f1', '672.g1'], 'contains': ['2688.a1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2816, 9125, 3153, 7778], 'generators': [479001600], 'label': '2688.ed.1344.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1344.a1', 'normal_contained_in': ['168.a1', '672.a1'], 'normal_contains': ['2688.a1'], 'normalizer': '1.a1', 'old_label': '1344.a1', 'projective_image': '1344.11307', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1344.11307', 'quotient_action_kernel_order': 1344, 'quotient_fusion': None, 'short_label': '1344.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282581
    {'ambient': '2688.ed', 'aut_centralizer_order': 10752, 'aut_label': '1344.b1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.b1', '448.b1', '672.a1', '672.b1', '672.c1', '672.h1', '672.i1', '672.j1', '672.k1'], 'contains': ['2688.a1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6112, 8438, 5750, 7179], 'generators': [3669120], 'label': '2688.ed.1344.b1', 'mobius_quo': -1, 'mobius_sub': 448, 'normal_closure': '1344.b1', 'normal_contained_in': ['168.c1', '672.a1', '672.b1', '672.c1'], 'normal_contains': ['2688.a1'], 'normalizer': '1.a1', 'old_label': '1344.b1', 'projective_image': '1344.11688', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1344.11688', 'quotient_action_kernel_order': 1344, 'quotient_fusion': None, 'short_label': '1344.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282582
    {'ambient': '2688.ed', 'aut_centralizer_order': 1344, 'aut_label': '1344.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.c1', '448.c1', '672.b1', '672.d1', '672.l1', '672.m1', '672.n1'], 'contains': ['2688.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2051, -1, 3060, -1], 'generators': [40320], 'label': '2688.ed.1344.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '672.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '1344.c1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282583
    {'ambient': '2688.ed', 'aut_centralizer_order': 1536, 'aut_label': '1344.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['448.d1', '672.e1', '672.h1', '672.l1', '672.o1', '672.p1', '672.q1', '672.r1'], 'contains': ['2688.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2884, -1, 3246, -1], 'generators': [56566145405], 'label': '2688.ed.1344.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '336.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '1344.d1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282584
    {'ambient': '2688.ed', 'aut_centralizer_order': 1536, 'aut_label': '1344.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['448.e1', '672.f1', '672.h1', '672.m1', '672.o1', '672.s1', '672.t1'], 'contains': ['2688.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3806, -1, 3704, -1], 'generators': [56569814525], 'label': '2688.ed.1344.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '1344.e1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282585
    {'ambient': '2688.ed', 'aut_centralizer_order': 768, 'aut_label': '1344.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['448.f1', '672.e1', '672.f1', '672.i1', '672.n1', '672.p1', '672.s1', '672.u1'], 'contains': ['2688.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3132, -1, 3485, -1], 'generators': [57045147005], 'label': '2688.ed.1344.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '1344.f1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282586
    {'ambient': '2688.ed', 'aut_centralizer_order': 192, 'aut_label': '1344.g1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['448.g1', '672.g1', '672.j1', '672.l1', '672.m1', '672.n1', '672.q1', '672.t1', '672.u1'], 'contains': ['2688.a1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3451, -1, 3353, -1], 'generators': [56566185725], 'label': '2688.ed.1344.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '1344.g1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282587
    {'ambient': '2688.ed', 'aut_centralizer_order': None, 'aut_label': '2688.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['384.a1', '896.a1', '1344.a1', '1344.b1', '1344.c1', '1344.d1', '1344.e1', '1344.f1', '1344.g1'], 'contains': [], 'core': '2688.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2884, 8785, 3246, 7471], 'generators': [], 'label': '2688.ed.2688.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '2688.a1', 'normal_contained_in': ['336.d1', '1344.a1', '1344.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2688.a1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2688.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182282588
    {'ambient': '2688.ed', 'aut_centralizer_order': 2, 'aut_label': '14.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '192.1497', 'aut_weyl_index': 56, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['7.a1'], 'contains': ['28.i1', '28.j1', '28.l1', '28.m1', '28.n1', '42.g1', '56.m1'], 'core': '336.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [5657, -1, 6479, -1], 'generators': [69031838370, 75258822112, 63283818170, 62793166108, 44112103731, 3669120, 56566145405], 'label': '2688.ed.14.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.f1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.f1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282589
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '14.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '7.a1'], 'contains': ['28.j1', '28.k1', '28.l1', '28.n1', '28.o1', '42.c1', '56.l1'], 'core': '42.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [5312, -1, 5865, -1], 'generators': [69020185890, 1122, 56566145405, 56577757565, 3669120, 11652480, 81474230591], 'label': '2688.ed.14.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.g1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.g1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282590
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '168.b1', 'complements': ['168.b1', '168.j1', '168.v1', '168.o1', '168.t1', '168.bg1', '168.bf1', '168.p1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.d1'], 'contains': ['48.a1', '112.u1', '128.a1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [380, 8125, 423, 2542], 'generators': [81474226495, 69020185890, 1122, 56566145405, 81474230591], 'label': '2688.ed.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['48.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '2688.ed', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282591
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11307', 'aut_weyl_index': 8, 'centralizer': '336.b1', 'complements': ['1344.c1', '1344.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '6.b1', '14.e1', '16.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6213, 3580, 5176, 3904], 'generators': [56577758221, 63272165690, 1122, 3669120, 69020185890, 81474230591, 56566145405, 81474226495], 'label': '2688.ed.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '672.1256', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 182282592
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '168.20', 'aut_weyl_index': 64, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '8.c1'], 'contains': ['32.a1', '32.b1', '32.c1', '48.b1', '112.d1'], 'core': '336.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4392, -1, 3146, -1], 'generators': [57045187785, 50339123661, 479004131, 3669120, 50339121939], 'label': '2688.ed.16.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '16.b1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 182282593
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.20', 'aut_weyl_index': 64, 'centralizer': '336.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '8.c1'], 'contains': ['32.b1', '32.d1', '48.c1', '112.g1'], 'core': '336.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [6369, -1, 5371, -1], 'generators': [56577758221, 44591104203, 3669120, 44112104729, 69020185045], 'label': '2688.ed.16.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '16.c1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 182282594
    {'ambient': '2688.ed', 'aut_centralizer_order': 2, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '168.20', 'aut_weyl_index': 64, 'centralizer': '672.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '8.c1'], 'contains': ['32.c1', '32.d1', '48.d1', '112.l1'], 'core': '336.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [5420, -1, 5152, -1], 'generators': [56577758221, 3669120, 44112104729, 11652480, 69020185045], 'label': '2688.ed.16.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '16.d1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 182282595
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '21.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1344.4277', 'aut_weyl_index': 8, 'centralizer': '84.a1', 'complements': ['128.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '7.a1'], 'contains': ['42.a1', '42.b1', '42.c1', '42.d1', '42.e1', '42.f1', '42.g1'], 'core': '21.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7651, 1654, 7196, 9433], 'generators': [69020185890, 56566145405, 56577757565, 490654080, 3669120, 11652480, 81474230591], 'label': '2688.ed.21.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '21.a1', 'normal_contained_in': ['3.a1'], 'normal_contains': ['42.a1', '42.b1', '42.c1', '168.b1'], 'normalizer': '1.a1', 'old_label': '21.a1', 'projective_image': '672.1256', 'quotient_action_image': '21.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '21.a1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 182282596
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '168.b1', 'complements': ['112.l1', '112.k1', '112.p1'], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.a1', '12.d1'], 'contains': ['48.a1', '168.a1', '192.a1'], 'core': '24.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1195, 7227, 544, 3887], 'generators': [81474226495, 69020185890, 56566145405, 81953228095, 81474230591], 'label': '2688.ed.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['48.a1', '168.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '1344.11307', 'quotient_action_image': '3.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282597
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '24.b1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '168.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.a1', '12.b1', '12.c1'], 'contains': ['48.a1', '168.c1', '192.b1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3079, 5431, 2488, 5063], 'generators': [81474226495, 69020185890, 56566145405, 3669120, 81474230591], 'label': '2688.ed.24.b1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '24.b1', 'normal_contained_in': ['8.b1', '12.a1', '12.b1', '12.c1'], 'normal_contains': ['48.a1', '168.c1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282598
    {'ambient': '2688.ed', 'aut_centralizer_order': 7, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.890', 'aut_weyl_index': 56, 'centralizer': '96.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '8.c1'], 'contains': ['48.b1', '48.c1', '48.d1', '168.b1'], 'core': '168.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [7146, -1, 4894, -1], 'generators': [56577758221, 44602758809, 3669120, 44112104729, 11652480], 'label': '2688.ed.24.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '24.c1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282599
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '12.b1', '12.d1'], 'contains': ['48.a1', '168.bk1', '192.c1'], 'core': '48.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [888, -1, 302, -1], 'generators': [81474226495, 69020185890, 56566145405, 56566186381, 81474230591], 'label': '2688.ed.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.d1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282600
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.b1'], 'contains': ['56.a1', '56.b1', '56.c1', '56.s1', '56.t1', '84.d1', '112.b1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2319, -1, 1654, -1], 'generators': [69023855010, 57045187785, 56566145405, 50339123205, 63272166915, 81474230591], 'label': '2688.ed.28.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '28.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282601
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '14.b1'], 'contains': ['56.a1', '56.c1', '56.d1', '56.t1', '56.u1', '84.e1', '112.a1'], 'core': '168.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1553, -1, 1164, -1], 'generators': [69020185890, 57045187785, 56566145405, 50339123205, 81953228201, 81474230591], 'label': '2688.ed.28.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '28.b1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282602
    {'ambient': '2688.ed', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1344.11307', 'aut_weyl_index': 8, 'centralizer': '672.a1', 'complements': ['1344.a1', '1344.c1', '1344.g1', '1344.f1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '6.c1', '14.g1', '16.d1'], 'core': '2.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [5603, 2132, 5016, 5111], 'generators': [81474226495, 69020185890, 56577758221, 1122, 56566145405, 3669120, 11652480, 81474230591], 'label': '2688.ed.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '6.c1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '1344.11688', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '672.1256'}
  • id: 182282603
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['14.a1', '14.b1', '14.c1'], 'contains': ['56.a1', '56.i1', '56.k1', '84.g1', '112.d1'], 'core': '336.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4526, -1, 4211, -1], 'generators': [57045187785, 56566145405, 50339123205, 81953228201, 3669120, 81474230591], 'label': '2688.ed.28.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.c1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282604
    {'ambient': '2688.ed', 'aut_centralizer_order': 6, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '64.138', 'aut_weyl_index': 168, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1'], 'contains': ['56.e1', '56.f1', '56.g1', '56.h1', '56.j1', '56.l1', '56.m1', '84.h1'], 'core': '168.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [6101, -1, 6440, -1], 'generators': [63283818170, 44112103731, 11612160, 3669120, 11652480, 75247209952], 'label': '2688.ed.28.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '28.d1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282605
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['14.a1', '14.b1', '14.d1'], 'contains': ['56.c1', '56.i1', '56.o1', '84.k1', '112.f1'], 'core': '672.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4671, -1, 4423, -1], 'generators': [56566145405, 50339123205, 81953228201, 75726247012, 3669120, 81474230591], 'label': '2688.ed.28.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.e1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282606
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '168.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1', '14.d1', '14.e1'], 'contains': ['56.i1', '56.p1', '84.l1', '112.g1'], 'core': '336.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [5869, -1, 7377, -1], 'generators': [62793166108, 56566145405, 44112103731, 56577757565, 3669120, 63272165690], 'label': '2688.ed.28.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.f1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282607
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '168.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1', '14.e1'], 'contains': ['56.i1', '56.q1', '84.m1', '112.h1'], 'core': '672.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6830, -1, 5907, -1], 'generators': [75258822112, 63272165690, 62793166108, 44112103731, 3669120, 56566145405], 'label': '2688.ed.28.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.g1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282608
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '14.b1', '14.e1'], 'contains': ['56.b1', '56.d1', '56.i1', '56.n1', '56.r1', '84.a1', '112.e1'], 'core': '84.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2922, -1, 3401, -1], 'generators': [69020185890, 56566145405, 44112103731, 3669120, 63272165690, 81474230591], 'label': '2688.ed.28.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.h1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282609
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '28.i1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.49', 'aut_weyl_index': 224, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.b1', '14.f1'], 'contains': ['56.k1', '56.n1', '56.o1', '56.t1', '84.o1', '112.j1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [4301, -1, 3815, -1], 'generators': [56566145405, 50339123205, 75726247012, 3669120, 63272166915, 81474230591], 'label': '2688.ed.28.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.i1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.i1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282610
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '28.j1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '48.49', 'aut_weyl_index': 224, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['14.a1', '14.f1', '14.g1'], 'contains': ['56.k1', '56.o1', '56.q1', '84.p1', '112.k1'], 'core': '672.b1', 'coset_action_label': None, 'count': 56, 'diagramx': [5225, -1, 5456, -1], 'generators': [69020185890, 50339124835, 1122, 56577757565, 3669120, 11652480], 'label': '2688.ed.28.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.j1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.j1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282611
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '28.k1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '14.b1', '14.g1'], 'contains': ['56.k1', '56.o1', '56.r1', '56.s1', '56.u1', '84.b1', '112.i1'], 'core': '84.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3067, -1, 3163, -1], 'generators': [69020185890, 1122, 56566145405, 56566185725, 3669120, 81474230591], 'label': '2688.ed.28.k1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.k1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.k1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282612
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '28.l1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.c1', '14.f1', '14.g1'], 'contains': ['56.k1', '56.p1', '84.r1', '112.l1'], 'core': '336.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [5672, -1, 6667, -1], 'generators': [69020185890, 50339124835, 1122, 11612160, 3669120, 11652480], 'label': '2688.ed.28.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.l1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.l1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282613
    {'ambient': '2688.ed', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '672.a1', 'complements': ['896.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '21.a1', '24.c1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7310, 729, 4775, 7017], 'generators': [81964880575, 81474226495, 69020185890, 56577758221, 56566145405, 3669120, 11652480, 81474230591], 'label': '2688.ed.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.a1', '6.b1', '6.c1', '21.a1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '672.1256', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '672.1256'}
  • id: 182282614
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '28.m1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.49', 'aut_weyl_index': 224, 'centralizer': '168.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['14.e1', '14.f1'], 'contains': ['56.n1', '56.p1', '56.q1', '84.t1', '112.o1'], 'core': '672.c1', 'coset_action_label': None, 'count': 14, 'diagramx': [6529, -1, 6213, -1], 'generators': [75258822112, 62793166108, 44112103731, 3669120, 81953231628, 56566145405], 'label': '2688.ed.28.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.m1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.m1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282615
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '28.n1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '96.197', 'aut_weyl_index': 112, 'centralizer': '336.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.d1', '14.f1', '14.g1'], 'contains': ['56.o1', '56.p1', '84.u1', '112.p1'], 'core': '672.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [5475, -1, 7023, -1], 'generators': [69020185890, 50339124835, 1122, 56577797885, 11612160, 3669120], 'label': '2688.ed.28.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.n1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.n1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 182282616
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '28.o1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '14.e1', '14.g1'], 'contains': ['56.p1', '56.q1', '56.r1', '84.c1', '112.m1'], 'core': '84.c1', 'coset_action_label': None, 'count': 14, 'diagramx': [6332, -1, 5682, -1], 'generators': [69020185890, 1122, 56566145405, 56577757565, 3669120, 81474230591], 'label': '2688.ed.28.o1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.o1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.o1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282617
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '42.2', 'aut_weyl_index': 256, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '16.b1'], 'contains': ['64.a1', '64.c1', '96.a1', '224.a1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [592, -1, 209, -1], 'generators': [57045187785, 50339123661, 479004131, 50339121939], 'label': '2688.ed.32.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '32.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282618
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '42.2', 'aut_weyl_index': 256, 'centralizer': '168.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '16.b1', '16.c1'], 'contains': ['64.a1', '64.b1', '96.b1', '224.e1'], 'core': '672.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3814, -1, 3172, -1], 'generators': [81474226495, 1122, 3669120, 63272165690], 'label': '2688.ed.32.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '32.b1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282619
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '42.2', 'aut_weyl_index': 256, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '16.b1', '16.d1'], 'contains': ['64.b1', '64.c1', '96.c1', '224.f1'], 'core': '672.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [3639, -1, 2773, -1], 'generators': [56566186381, 3669120, 44112104729, 69020185045], 'label': '2688.ed.32.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '32.c1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 182282620
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '42.2', 'aut_weyl_index': 256, 'centralizer': '336.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '16.c1', '16.d1'], 'contains': ['64.b1', '96.d1', '224.j1'], 'core': '672.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [5018, -1, 5574, -1], 'generators': [56577758221, 3669120, 44112104729, 69020185045], 'label': '2688.ed.32.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '32.d1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 182282621
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '42.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '168.20', 'aut_weyl_index': 64, 'centralizer': '42.a1', 'complements': ['64.c1'], 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '14.b1', '21.a1'], 'contains': ['84.a1', '84.b1', '84.d1', '84.e1', '84.g1', '84.k1', '84.o1'], 'core': '42.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3478, 3826, 3528, 7179], 'generators': [69020185890, 57045187325, 56566145405, 479001600, 3669120, 81474230591], 'label': '2688.ed.42.a1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.a1', 'normal_contained_in': ['6.a1', '21.a1'], 'normal_contains': ['84.a1', '84.b1', '336.a1'], 'normalizer': '1.a1', 'old_label': '42.a1', 'projective_image': '672.1256', 'quotient_action_image': '42.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '42.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 182282622
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '42.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.20', 'aut_weyl_index': 64, 'centralizer': '42.b1', 'complements': ['64.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '14.e1', '21.a1'], 'contains': ['84.a1', '84.c1', '84.l1', '84.m1', '84.t1'], 'core': '42.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8019, 2378, 7180, 8151], 'generators': [69020185890, 56566145405, 56577757565, 479001600, 3669120, 81474230591], 'label': '2688.ed.42.b1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.b1', 'normal_contained_in': ['6.b1', '21.a1'], 'normal_contains': ['84.a1', '84.c1', '336.b1'], 'normalizer': '1.a1', 'old_label': '42.b1', 'projective_image': '672.1256', 'quotient_action_image': '42.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '42.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 182282623
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '42.c1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '168.20', 'aut_weyl_index': 64, 'centralizer': '84.a1', 'complements': ['64.a1', '64.c1'], 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '14.g1', '21.a1'], 'contains': ['84.b1', '84.c1', '84.p1', '84.r1', '84.u1'], 'core': '42.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7542, 930, 6865, 9433], 'generators': [69020185890, 56566145405, 56577757565, 3669120, 11652480, 81474230591], 'label': '2688.ed.42.c1', 'mobius_quo': 0, 'mobius_sub': -7, 'normal_closure': '42.c1', 'normal_contained_in': ['6.c1', '21.a1'], 'normal_contains': ['84.b1', '84.c1', '336.c1'], 'normalizer': '1.a1', 'old_label': '42.c1', 'projective_image': '1344.11688', 'quotient_action_image': '21.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '42.c1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 182282624
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '336.210', 'aut_weyl_index': 32, 'centralizer': '168.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '12.a1', '28.h1', '32.b1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3246, 8043, 3180, 685], 'generators': [81474226495, 69020185890, 1122, 56566145405, 3669120, 63272165690, 81474230591], 'label': '2688.ed.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282625
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '96.167', 'aut_weyl_index': 112, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['14.a1', '21.a1'], 'contains': ['84.f1', '84.g1', '84.j1', '84.k1', '84.m1', '84.n1', '84.p1'], 'core': '336.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7689, -1, 7615, -1], 'generators': [56566145405, 75258822112, 490654080, 3669120, 11652480, 81474230591], 'label': '2688.ed.42.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '42.d1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282645
    {'ambient': '2688.ed', 'aut_centralizer_order': 12, 'aut_label': '56.l1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.g1', '28.d1'], 'contains': ['112.i1', '112.k1', '112.l1', '112.m1', '112.p1', '168.u1'], 'core': '336.c1', 'coset_action_label': None, 'count': 112, 'diagramx': [5974, -1, 6030, -1], 'generators': [1122, 56566145405, 56577757565, 3669120, 11652480], 'label': '2688.ed.56.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '56.l1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282626
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.890', 'aut_weyl_index': 56, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1', '21.a1'], 'contains': ['84.f1', '84.g1', '84.h1', '84.i1', '84.l1', '84.q1', '84.r1'], 'core': '168.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [7873, -1, 7983, -1], 'generators': [56566145405, 56577757565, 490654080, 3669120, 11652480, 81474230591], 'label': '2688.ed.42.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '42.e1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282627
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.890', 'aut_weyl_index': 56, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.d1', '21.a1'], 'contains': ['84.i1', '84.j1', '84.k1', '84.l1', '84.s1', '84.u1'], 'core': '336.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [8569, -1, 8237, -1], 'generators': [69510839970, 56566145405, 56577757565, 69031838370, 3669120, 81474230591], 'label': '2688.ed.42.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '42.f1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282628
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '42.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.45', 'aut_weyl_index': 224, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.f1', '21.a1'], 'contains': ['84.n1', '84.o1', '84.p1', '84.q1', '84.r1', '84.s1', '84.t1', '84.u1'], 'core': '336.c1', 'coset_action_label': None, 'count': 28, 'diagramx': [8258, -1, 7814, -1], 'generators': [56566145405, 75258822112, 69031838370, 490654080, 3669120, 81474230591], 'label': '2688.ed.42.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '42.g1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.g1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282629
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '168.b1', 'complements': ['56.g1', '56.m1', '56.j1', '56.f1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.b1', '24.d1'], 'contains': ['336.d1', '384.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [411, 7493, 29, 4447], 'generators': [81474226495, 69020185890, 56566145405, 81474230591], 'label': '2688.ed.48.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.a1', '24.b1'], 'normal_contains': ['336.d1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '2688.ed', 'quotient_action_image': '3.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282630
    {'ambient': '2688.ed', 'aut_centralizer_order': 28, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '16.b1', '24.c1'], 'contains': ['96.a1', '96.b1', '96.c1', '336.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4937, -1, 2972, -1], 'generators': [75247206450, 3669120, 75726208050, 57045185723], 'label': '2688.ed.48.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.b1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282631
    {'ambient': '2688.ed', 'aut_centralizer_order': 56, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '48.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '16.c1', '24.c1'], 'contains': ['96.b1', '96.d1', '336.b1'], 'core': '336.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [7201, -1, 5356, -1], 'generators': [56577758221, 44591106329, 3669120, 44112104729], 'label': '2688.ed.48.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.c1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282632
    {'ambient': '2688.ed', 'aut_centralizer_order': 14, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '96.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '16.d1', '24.c1'], 'contains': ['96.c1', '96.d1', '336.c1'], 'core': '336.c1', 'coset_action_label': None, 'count': 32, 'diagramx': [6989, -1, 5195, -1], 'generators': [56577758221, 3669120, 44112104729, 11652480], 'label': '2688.ed.48.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.d1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 182282633
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.a1', '28.b1', '28.c1'], 'contains': ['112.c1', '112.q1', '168.e1', '224.a1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1189, -1, 1164, -1], 'generators': [57045187785, 56566145405, 50339123205, 81953228201, 81474230591], 'label': '2688.ed.56.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '56.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282634
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.a1', '28.h1'], 'contains': ['112.c1', '112.r1', '112.s1', '168.g1', '224.c1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2281, -1, 1961, -1], 'generators': [69023855010, 62793166108, 44112103731, 81953231628, 56566145405], 'label': '2688.ed.56.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.b1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282635
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '336.210', 'aut_weyl_index': 32, 'centralizer': '336.a1', 'complements': ['672.d1', '672.n1', '672.g1', '672.u1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.b1', '8.d1', '12.b1', '28.k1', '32.c1'], 'core': '4.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3071, 6329, 2660, 2201], 'generators': [81474226495, 69020185890, 1122, 56566145405, 56566186381, 3669120, 81474230591], 'label': '2688.ed.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.b1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '1344.11688', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 182282636
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.a1', '28.b1', '28.e1'], 'contains': ['112.c1', '112.t1', '168.h1', '224.d1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2136, -1, 1498, -1], 'generators': [56566145405, 50339123205, 81953228201, 75726247012, 81474230591], 'label': '2688.ed.56.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '56.c1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282637
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '28.b1', '28.h1'], 'contains': ['112.c1', '112.s1', '112.u1', '168.a1', '224.b1'], 'core': '168.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1334, -1, 956, -1], 'generators': [69020185890, 56566145405, 44112103731, 63272165690, 81474230591], 'label': '2688.ed.56.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.d1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282638
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['14.b1', '28.d1'], 'contains': ['112.a1', '112.b1', '112.d1', '112.e1', '112.f1', '112.i1', '112.j1', '168.i1'], 'core': '336.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3702, -1, 4423, -1], 'generators': [81474228973, 57045187785, 57045147465, 62793166108, 3669120], 'label': '2688.ed.56.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '56.e1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282639
    {'ambient': '2688.ed', 'aut_centralizer_order': 6, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '32.27', 'aut_weyl_index': 336, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['14.a1', '28.d1'], 'contains': ['112.d1', '112.f1', '112.h1', '112.k1', '168.j1'], 'core': '336.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [5471, -1, 5801, -1], 'generators': [63283818170, 44112103731, 75258822112, 3669120, 11652480], 'label': '2688.ed.56.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '56.f1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282640
    {'ambient': '2688.ed', 'aut_centralizer_order': 6, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '64.138', 'aut_weyl_index': 168, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '14.c1', '28.d1'], 'contains': ['112.d1', '112.g1', '112.l1', '168.b1'], 'core': '168.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [6737, -1, 6563, -1], 'generators': [63283818170, 44112103731, 11612160, 3669120, 11652480], 'label': '2688.ed.56.g1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '56.g1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282641
    {'ambient': '2688.ed', 'aut_centralizer_order': 48, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1344, 'centralizer': '56.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.e1', '28.d1'], 'contains': ['112.e1', '112.g1', '112.h1', '112.m1', '112.o1', '168.l1'], 'core': '336.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [6587, -1, 6203, -1], 'generators': [44112103731, 11612160, 3669120, 75247209952, 63272165690], 'label': '2688.ed.56.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '56.h1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182282642
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1', '28.e1', '28.f1', '28.g1', '28.h1'], 'contains': ['112.c1', '112.n1', '168.n1', '224.e1'], 'core': '672.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4637, -1, 4127, -1], 'generators': [62793166108, 56566145405, 44112103731, 3669120, 63272165690], 'label': '2688.ed.56.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.i1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282643
    {'ambient': '2688.ed', 'aut_centralizer_order': 6, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '64.138', 'aut_weyl_index': 168, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.d1', '28.d1'], 'contains': ['112.f1', '112.g1', '112.p1', '168.o1'], 'core': '336.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [6361, -1, 7106, -1], 'generators': [56566142764, 81964884108, 75258862432, 11612160, 3669120], 'label': '2688.ed.56.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '56.j1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282644
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.c1', '28.i1', '28.j1', '28.k1', '28.l1'], 'contains': ['112.n1', '112.q1', '168.s1', '224.f1'], 'core': '672.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [4134, -1, 3792, -1], 'generators': [69020185890, 50339124835, 40320, 1122, 3669120], 'label': '2688.ed.56.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.k1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282646
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '336.210', 'aut_weyl_index': 32, 'centralizer': '336.b1', 'complements': ['672.d1', '672.n1', '672.g1', '672.u1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.c1'], 'contains': ['8.b1', '12.c1', '28.o1', '32.d1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5776, 4028, 5171, 3928], 'generators': [81474226495, 69020185890, 56577758221, 1122, 56566145405, 3669120, 81474230591], 'label': '2688.ed.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.c1'], 'normal_contains': ['8.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '1344.11688', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 182282647
    {'ambient': '2688.ed', 'aut_centralizer_order': 6, 'aut_label': '56.m1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '16.11', 'aut_weyl_index': 672, 'centralizer': '112.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.f1', '28.d1'], 'contains': ['112.j1', '112.k1', '112.l1', '112.o1', '112.p1', '168.v1'], 'core': '336.c1', 'coset_action_label': None, 'count': 112, 'diagramx': [6186, -1, 6416, -1], 'generators': [63283818170, 44112103731, 75258862432, 11612160, 3669120], 'label': '2688.ed.56.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1', 'old_label': '56.m1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282648
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '56.n1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.h1', '28.i1', '28.m1'], 'contains': ['112.n1', '112.s1', '168.bb1', '224.h1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [3918, -1, 3544, -1], 'generators': [81953231628, 62793166108, 56566145405, 44112103731, 3669120], 'label': '2688.ed.56.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.n1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.n1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282649
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '56.o1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.e1', '28.i1', '28.j1', '28.k1', '28.n1'], 'contains': ['112.n1', '112.t1', '168.bc1', '224.i1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [4351, -1, 3959, -1], 'generators': [69020185890, 50339124835, 1122, 56566185725, 3669120], 'label': '2688.ed.56.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.o1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.o1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282650
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '56.p1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.f1', '28.l1', '28.m1', '28.n1', '28.o1'], 'contains': ['112.n1', '168.bd1', '224.j1'], 'core': '672.c1', 'coset_action_label': None, 'count': 14, 'diagramx': [5634, -1, 6919, -1], 'generators': [69020185890, 50339124835, 1122, 11612160, 3669120], 'label': '2688.ed.56.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.p1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.p1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282651
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '56.q1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '168.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.g1', '28.j1', '28.m1', '28.o1'], 'contains': ['112.n1', '168.be1', '224.k1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [6900, -1, 5655, -1], 'generators': [69020185890, 50339124835, 1122, 56577757565, 3669120], 'label': '2688.ed.56.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.q1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.q1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 182282652
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '56.r1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '84.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '28.h1', '28.k1', '28.o1'], 'contains': ['112.n1', '112.r1', '112.u1', '168.c1', '224.g1'], 'core': '168.c1', 'coset_action_label': None, 'count': 7, 'diagramx': [2705, -1, 2874, -1], 'generators': [69020185890, 1122, 56566145405, 3669120, 81474230591], 'label': '2688.ed.56.r1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.r1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.r1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282653
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '56.s1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.a1', '28.k1'], 'contains': ['112.q1', '112.r1', '112.t1', '168.bi1', '224.m1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2462, -1, 1706, -1], 'generators': [69020185890, 50339124835, 56569814525, 40320, 1122], 'label': '2688.ed.56.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '56.s1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.s1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282654
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '56.t1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['28.a1', '28.b1', '28.i1'], 'contains': ['112.q1', '112.s1', '112.t1', '168.bj1', '224.n1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [1530, -1, 1331, -1], 'generators': [56566145405, 50339123205, 75726247012, 63272166915, 81474230591], 'label': '2688.ed.56.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '56.t1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.t1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282655
    {'ambient': '2688.ed', 'aut_centralizer_order': 16, 'aut_label': '56.u1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '168.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '28.b1', '28.k1'], 'contains': ['112.q1', '112.t1', '112.u1', '168.bk1', '224.l1'], 'core': '336.d1', 'coset_action_label': None, 'count': 56, 'diagramx': [843, -1, 765, -1], 'generators': [69020185890, 1122, 56566145405, 56566185725, 81474230591], 'label': '2688.ed.56.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '56.u1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.u1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182282656
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '168.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '32.a1', '32.b1'], 'contains': ['128.a1', '192.a1', '448.a1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [452, -1, 561, -1], 'generators': [81474226495, 1122, 63272165690], 'label': '2688.ed.64.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '64.a1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282657
    {'ambient': '2688.ed', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '336.210', 'aut_weyl_index': 32, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.d1', '12.d1', '28.b1', '32.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1132, -1, 657, -1], 'generators': [81474226495, 69020185890, 57045187785, 1122, 56566145405, 63272165690, 81474230591], 'label': '2688.ed.4.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.d1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182282658
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '168.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '32.b1', '32.c1', '32.d1'], 'contains': ['128.a1', '192.b1', '448.b1'], 'core': '1344.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3280, -1, 2824, -1], 'generators': [81474226495, 1122, 3669120], 'label': '2688.ed.64.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '64.b1', 'projective_image': '1344.11688', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282659
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '336.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '32.a1', '32.c1'], 'contains': ['128.a1', '192.c1', '448.c1'], 'core': '2688.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [100, -1, 207, -1], 'generators': [56566186381, 44112104729, 69020185045], 'label': '2688.ed.64.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '64.c1', 'projective_image': '2688.ed', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282660
    {'ambient': '2688.ed', 'aut_centralizer_order': 256, 'aut_label': '84.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '42.2', 'aut_weyl_index': 256, 'centralizer': '21.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '28.h1', '42.a1', '42.b1'], 'contains': ['168.a1', '168.c1', '168.g1', '168.n1', '168.bb1'], 'core': '84.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3177, 4588, 3401, 6246], 'generators': [69020185890, 56566145405, 479001600, 3669120, 81474230591], 'label': '2688.ed.84.a1', 'mobius_quo': -2, 'mobius_sub': 14, 'normal_closure': '84.a1', 'normal_contained_in': ['12.a1', '42.a1', '42.b1'], 'normal_contains': ['168.a1', '168.c1', '672.a1'], 'normalizer': '1.a1', 'old_label': '84.a1', 'projective_image': '672.1256', 'quotient_action_image': '21.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '84.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282661
    {'ambient': '2688.ed', 'aut_centralizer_order': 64, 'aut_label': '84.b1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '42.2', 'aut_weyl_index': 256, 'centralizer': '42.a1', 'complements': ['32.a1'], 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '28.k1', '42.a1', '42.c1'], 'contains': ['168.c1', '168.s1', '168.bc1', '168.bi1', '168.bk1'], 'core': '84.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3065, 3708, 3001, 7065], 'generators': [69020185890, 56566145405, 56566185725, 3669120, 81474230591], 'label': '2688.ed.84.b1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.b1', 'normal_contained_in': ['12.b1', '42.a1', '42.c1'], 'normal_contains': ['168.c1', '672.b1'], 'normalizer': '1.a1', 'old_label': '84.b1', 'projective_image': '1344.11688', 'quotient_action_image': '42.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '84.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 182282662
    {'ambient': '2688.ed', 'aut_centralizer_order': 128, 'aut_label': '84.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '42.2', 'aut_weyl_index': 256, 'centralizer': '42.b1', 'complements': ['32.a1'], 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '28.o1', '42.b1', '42.c1'], 'contains': ['168.c1', '168.bd1', '168.be1'], 'core': '84.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [7421, 2433, 6762, 8111], 'generators': [69020185890, 56566145405, 56577757565, 3669120, 81474230591], 'label': '2688.ed.84.c1', 'mobius_quo': 0, 'mobius_sub': 14, 'normal_closure': '84.c1', 'normal_contained_in': ['12.c1', '42.b1', '42.c1'], 'normal_contains': ['168.c1', '672.c1'], 'normalizer': '1.a1', 'old_label': '84.c1', 'projective_image': '1344.11688', 'quotient_action_image': '42.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '84.c1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 182282663
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.a1', '42.a1'], 'contains': ['168.d1', '168.e1', '168.f1', '168.g1', '168.h1', '168.bh1', '168.bi1', '168.bj1'], 'core': '1344.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2797, -1, 2605, -1], 'generators': [69023855010, 57045187325, 56566145405, 479001600, 81474230591], 'label': '2688.ed.84.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '84.d1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182282664
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '42.2', 'aut_weyl_index': 256, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '28.b1', '42.a1'], 'contains': ['168.a1', '168.e1', '168.h1', '168.bj1', '168.bk1'], 'core': '168.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2127, -1, 1834, -1], 'generators': [69020185890, 57045187325, 56566145405, 479001600, 81474230591], 'label': '2688.ed.84.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '84.e1', 'projective_image': '1344.11307', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182282665
    {'ambient': '2688.ed', 'aut_centralizer_order': 8, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.27', 'aut_weyl_index': 336, 'centralizer': '84.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['42.d1', '42.e1'], 'contains': ['168.i1', '168.j1', '168.k1', '168.m1', '168.p1', '168.r1', '168.t1'], 'core': '336.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [7898, -1, 8491, -1], 'generators': [56566145405, 50350736995, 490654080, 3669120, 11652480], 'label': '2688.ed.84.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.f1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182282666
    {'ambient': '2688.ed', 'aut_centralizer_order': 32, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.10', 'aut_weyl_index': 448, 'centralizer': '42.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['28.c1', '42.a1', '42.d1', '42.e1'], 'contains': ['168.d1', '168.e1', '168.i1', '168.k1', '168.n1', '168.q1', '168.s1'], 'core': '336.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5591, -1, 4593, -1], 'generators': [57045187325, 56566145405, 479001600, 3669120, 81474230591], 'label': '2688.ed.84.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.g1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 182282667
    {'ambient': '2688.ed', 'aut_centralizer_order': 24, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.138', 'aut_weyl_index': 168, 'centralizer': '28.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.d1', '42.e1'], 'contains': ['168.b1', '168.i1', '168.j1', '168.l1', '168.o1', '168.u1', '168.v1'], 'core': '168.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [7716, -1, 7644, -1], 'generators': [56566145405, 56577757565, 490654080, 3669120, 11652480], 'label': '2688.ed.84.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '84.h1', 'projective_image': '672.1256', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}